LIST OF CITATIONS of publications by Goulnara N. ARZHANTSEVA
more then 220 citations in total, excluding self-citations and citations of the paper with A. Yu. Ol'shanskii (PhD supervisor).
Last update: Aug. 26, 2011
Papers already published or accepted:
Summary and comments to my list of publications
[1] G.N. Arzhantseva and E.
Guentner, Coarse non-amenability and covers with small
eigenvalues,
Mathematische Annalen (2011), to appear. pdf
NEW !
[2] G.N. Arzhantseva,
M. Bridson,
T. Januszkiewicz,
I.
Leary, A. Minasyan,
J. Swiatkowski,
Infinite
groups with fixed point properties,
Geometry &
Topology, 13 (2009), 1229-1263. pdf
11
citations by
M. Bridson, On the dimension of CAT(0) spaces where mapping class groups act, (2009), arXiv.org:0908.0690
M. Bridson, K. Vogtmann, Actions of automorphism groups of free groups on homology spheres and acyclic manifolds, (2008), arXiv.org:0803.2062
I. Chatterji, M. Kassabov, New examples of finitely presented groups with strong fixed point properties, (2008), arXiv.org:0809.3719, to appear in Journal of Topology and Analysis.
D. Fisher, L. Silberman, Groups not acting on manifolds, Int. Math. Res. Not. 16 (2008), 11 pp.
G. Gandini, Cohomological invariants and the classifying space for proper actions, (2011), arXiv.org:1106.3022
T. Januszkiewicz, P.H. Kropholler, I.J. Leary, Groups possessing extensive hierarchical decompositions, (2009), arXiv.org:0908.3669
A. Naor, L.
Silberman,
Poincaré
inequalities, embeddings, and wild groups, (2010), arXiv.org:1005.4084
D.
Osajda,
A
construction of hyperbolic Coxeter
groups, (2010),
arXiv.org:
1003.0774
D.
Osajda,
P. Przytycki,
Boundaries of
systolic groups, Geom. Topol.
13
(2009), no. 5, 2807-2880.
D. Osin,
Small cancellations over
relatively hyperbolic
groups and embedding theorems, Annals of
Mathematics, 172 (2010), 1-39.
Sh. Weinberger,
Some remarks inspired by
the C0
Zimmer program,
(2009), preprint.
[3] G.N. Arzhantseva,
C. Drutu,
and M. Sapir, Compression
functions of uniform
embeddings of groups into
Hilbert
and Banach
spaces, Journal für
die Reine
und Angewandte
Mathematik,
[Crelle's
Journal], 633 (2009), 213-235. pdf
11
citations by
C.
Anantharaman-Delaroche,
Amenability
and exactness for groups, group actions and operator algebras, (2007)
http://www.univ-orleans.fr/mapmo/membres/anantharaman/publications/ESI07.pdf
T. Austin,
A.
Naor,
Y. Peres, The wreath product of
Z
with Z
has Hilbert compression
exponent 2/3,
Proc. Amer. Math. Soc. 137 (2009), no. 1, 85-90.
T. Austin, A
finitely-generated amenable group with very poor compression into Lebesgue
spaces, (2009),
arXiv.org:0909.2047
J.-C. Birget,
One-way permutations,
computational asymmetry
and distortion, J. Algebra 320
(2008), no. 11, 4030-4062.
A. Dranishnikov, M. Sapir, On the dimension growth of groups, (2010), arXiv:1008.3868
D.
Dreesen,
Hilbert
space compression for free products and
HNN-extension,
(2010), arXiv:1002.3879
S.
Gal, Asymptotic
dimension and uniform embeddings,
Groups Geom. Dyn.
2 (2008), no. 1,
63-84.
MR2367208
(2009d:20105)
A. Naor,
Y. Peres, Embeddings of
discrete groups and the speed of random walks,
Int. Math. Res. Not. IMRN
(2008), Art. ID rnn
076, 34 pp.
A. Naor, Y. Peres, Lp compression, traveling salesmen, and stable walks, arXiv.org:0904.4728
P. Nowak, G. Yu, Large-scale geometry, (2010), EMS publishing house, to appear, http://www.math.tamu.edu/~pnowak/book_etb/book_etb.pdf
M. Sapir, Some group theory problems, Internat. J. Algebra Comput. 17 (2007), no. 5-6, 1189-1214.
[4] G.N. Arzhantseva,
V.S. Guba,
M. Lustig
and J.-Ph. Préaux,
Testing Cayley
graph
densities,
Annales
mathematiques
Blaise
Pascal, 15(2) (2008), 169-221. abs
pdf
1
citation by
J. Cannon, Amenability, Folner sets, and Cooling Functions, (2009).
[5] G.N. Arzhantseva, A.
Minasyan
and D. Osin,
The
SQ-universality and residual properties
of
relatively
hyperbolic groups, Journal of
Algebra, 315(1)
(2007),
165-177. pdf
18
citations by
I. Belegradek, Rigidity and relative hyperbolicity of real hyperbolic hyperplane complements, (2007), arXiv.org:0711.2324
I. Belegradek, D. Osin, Rips construction and Kazhdan property (T), Groups Geom. Dyn. 2 (2008), no. 1, 1-12. MR2367206 (2009c:20076)
I. Belegradek, A. Szczepanski, Endomorphisms of relatively hyperbolic groups, with an appendix by Oleg V. Belegradek. Internat. J. Algebra Comput. 18 (2008), no. 1, 97-110. MR2394723 (2009a:20069)
D. Bisch,
R. Nicoara,
J. O. Button, Large groups of deficiency 1, Israel J. Math. 167 (2008), 111-140. MR2448020 (2009k:20068)
P.-E. Caprace,
N. Monod, Isometry
groups of
non-positively curved spaces: discrete subgroups,
J. Topology
2
(2009), no. 4,
701-746. MR2574741
M. Edjvet,
A. Vdovina,
On
the SQ-universality of groups with
special presentations, J.
Group Theory
(2010),
1433-5883.
D. Fisher, L. Silberman, Groups not acting on manifolds, Int. Math. Res. Not. IMRN 2008, no. 16, Art. ID rnn060, 11 pp. MR2435750 (2009f:57059)
Le Thi Giang, The relative hyperbolicity of one-relator relative presentations, J. Group Theory 12 (2009), no. 6, 949-959. MR2582060
T. Januszkiewicz, P. Kropholler, I. Leary, Groups possessing extensive hierarchical decompositions, (2009), arXiv.org:0908.3669
Ant. A. Klyachko, SQ-universality of one-relator relative presentations, Sb. Math. 197 (2006), no. 9-10, 1489-1508. MR2310117 (2008a:20040)
E. Martinez-Pedroza, On quasiconvexity and relative hyperbolic structures, (2008), arXiv.org:0811.2384
A. Minasyan, Groups with finitely many conjugacy classes and their automorphisms, Comment. Math. Helv. 84 (2009), no. 2, 259-296. MR2495795
A. Minasyan,
D. Osin,
A. Ol'shanskii, D. Osin,
M. Sapir, Lacunary
hyperbolic groups, Geom. Topol.
13
(2009), no. 4, 2051-2140.
MR2507115
D. Osin,
Small cancellations over
relatively hyperbolic
groups and embedding theorems, Annals of
Mathematics, 172 (2010), 1-39.
D. Osin,
On
the universal
theory of torsion and lacunary
hyperbolic groups,
(2009), arXiv.org:0903.3978
D. Witte
Morris, Introduction
to arithmetic groups, (2008),
arXiv:math/0106063
[6] G. N. Arzhantseva
and Z.Sunic,
Construction of elements in the
closure of Grigorchuk
group, Geometriae
Dedicata,
124(1)
(2007),
17-26. pdf
2
citations by
B. Demir,
M. Saltan,
On
p-adic
integers and the adding machine group,
(2010), arXiv:1007.0366
O.
Siegenthaler,
Discrete
and
Profinite
Groups Acting on Regular Rooted Trees,
PhD thesis, Georg-August-Universität
Göttingen,
2009,
http://webdoc.sub.gwdg.de/diss/2010/siegenthaler/siegenthaler.pdf
[7] G.N.
Arzhantseva, A.
Minasyan,
Relatively
hyperbolic groups are C*-simple,
Journal of Functional
Analysis, 243(1) (2007), 345-351.
pdf
3
citations by
P. de la Harpe, On simplicity of reduced C*-algebras of groups, Bull. Lond. Math. Soc. 39 (2007), no. 1, 1-26. MR2303514 (2008a:22004)
E. Martínez-Pedroza, Combination of quasiconvex subgroups of relatively hyperbolic groups, Groups Geom. Dyn. 3 (2009), no. 2, 317-342. MR2486802
E. Martinez-Pedroza, On quasiconvexity and relative hyperbolic structures, (2008), arXiv.org:0811.2384
[8] G.N. Arzhantseva,
P. de la Harpe,
D. Kahrobaei,
The true prosoluble
completion of a group:
Examples
and open problems, Geometriae
Dedicata,
124(1)
(2007),
5-17. abs
pdf.
4
citations by
K.
Bencsath,
A. Douglas, D. Kahrobaei,
Some
Residually
Solvable One-Relator
Groups, Irish
Math. Soc. Bulletin 65
(2010), 23-31.
S. Friedl, S.Vidussi, Twisted Alexander polynomials and fibered 3-manifolds, 2010, arXiv:1001.0132
D. Kahrobaei, Doubles of residually solvable groups in B. Fine, G. Rosenberger, D. Spellman (eds), Aspects of Infinite Group Theory, Algebra and Discrete Mathematics, World Scientific, 1 (2008), 192-200.
O.
Siegenthaler,
Discrete
and
Profinite
Groups Acting on Regular Rooted Trees,
PhD thesis, Georg-August-Universität
Göttingen,
2009,
http://webdoc.sub.gwdg.de/diss/2010/siegenthaler/siegenthaler.pdf
[9] G.N. Arzhantseva,
V.S. Guba,
M.V. Sapir, Metrics on diagram
groups and uniform
embeddings in a Hilbert space,
Commentarii
Mathematici
Helvetici,
81(4) (2006), 911-929. abs
pdf.
24
citations by
C.
Anantharaman-Delaroche,
Amenability
and exactness for groups, group actions and operator algebras,(2007)
http://www.univ-orleans.fr/mapmo/membres/anantharaman/publications/ESI07.pdf
T. Austin,
A.
Naor,
Y. Peres, The wreath product
of Z with Z has
Hilbert compression exponent 2/3,
Proc. Amer. Math. Soc. 137 (2009), no. 1,
85-90.
T. Austin, A
finitely-generated amenable group with very poor compression into Lebesgue
spaces, (2009),
arxiv.org:0909.2047
J.-C. Birget,
One-way permutations,
computational asymmetry
and distortion, J. Algebra 320
(2008), no. 11, 4030-4062.
N. Brodskiy,
D. Sonkin,
Compression of uniform
embeddings into
Hilbert space, Topology Appl.
155 (2008), no. 7,
725-732. MR2395586 (2009b:20078)
S. J.
Campbell, Property A and
affine buildings, J. Funct. Anal.
256
(2009), no. 2, 409-431.
Y. de Cornulier,
Y. Stalder,
A. Valette,
Proper actions of wreath
products and
generalizations, (2009),
arxiv.org:0905.3960
A.
Dranishnikov,
M.
Sapir,
On
the dimension growth of groups,
(2010), arxiv:1008.3868
D.
Dreesen, Hilbert
space compression under direct limits and
certain group extensions (2010),
arxiv.org:1009.2014
S.
Gal, Asymptotic
dimension and uniform embeddings,
Groups Geom. Dyn.
2 (2008), no. 1, 63-84.
V. Guba,
M.Sapir,
Diagram
groups and directed 2-complexes: homotopy
and
homology, J. Pure Appl.
Algebra 205 (2006),
no. 1, 1-47. MR2193190 2006j:20056
V.
Guba,
M.
Sapir,
On
the conjugacy
growth functions of groups,
(2010), arXiv:1003.1293v2
U.
Haagerup,
G. Picioroaga,
New Presentations of Thompson's
group
and applications, preprint (14
pp., 2008), arXiv:0812.0037,
to appear in J. of
Operator Theory.
S. Li,
Compression bounds for wreath
products, Proc.
Amer. Math. Soc. 138
(2010), no. 8,
2701-2714.
MR2644886
A. Naor,
Y. Peres, Lp
compression, traveling
salesmen, and stable walks, (2009),
arXiv:0904.4728
A. Naor,
Y. Peres, Embeddings
of discrete groups and the speed of random walks,
Int. Math. Res. Not. IMRN 2008, Art. ID rnn
076, 34 pp.
P. Nowak, On
exactness and isoperimetric profiles of
discrete groups, J. Funct.
Anal.
243 (2007), no. 1, 323-344. MR2291440 (2008c:20081)
P. Nowak, G. Yu, Large-Scale geometry, (2010), EMS publishing house, to appear, http://www.math.tamu.edu/~pnowak/book_etb/book_etb.pdf
S. Passidis, A. Weston, Manifestations of non linear roundness in analysis, discrete geometry and topology, in Limits of graphs in group theory and computer science by G. Arzhantseva, A.Valette (eds.), EPFL press, 2009.
M. Sapir, Some group theory problems, Internat. J. Algebra Comput. 17 (2007), no. 5-6, 1189-1214.
Y. Stalder, A. Valette, Wreath products with the integers, proper actions and Hilbert space compression, Geom. Dedicata 124 (2007), 199-211.
R. Tessera, Quantitative property A, Poincaré inequalities, Lp-compression and Lp-distortion for metric measure spaces, Geom. Dedicata 136 (2008), 203-220. MR2443353
R. Tessera, Asymptotic isoperimetry on groups and uniform embeddings into Banach spaces, (2006), arXiv.org:math/0603138
G. Yu, Higher index theory of elliptic operators and geometry of groups. International Congress of Mathematicians. Vol. II, 1623-1639, Eur. Math. Soc., Zürich, 2006.
[10]
G.N. Arzhantseva,
A dichotomy for
finitely generated subgroups of word hyperbolic groups,
Contemporary
Mathematics, 394, Amer. Math.Soc.,
5
citations by
M. Gromov, Singularities, expanders and topology of maps. I. Homology versus volume in the spaces of cycles. Geom. Funct. Anal. 19 (2009), no. 3, 743-841. MR2563769
I. Kapovich, P. Schupp, Random quotients of the modular group are rigid and essentially incompressible, J. Reine Angew. Math. 628 (2009), 91-119. MR2503236
I. Kapovich, P. Schupp, Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups, Math. Ann. 331 (2005), no. 1, 1-19. MR2107437 (2005h:20079)
I. Kapovich, R. Weidmann, Nielsen methods and groups acting on hyperbolic spaces, Geom. Dedicata 98 (2003), 95-121. MR1988426 (2004e:20076)
H. Reza Rostami, About groups with property (U), Armenian journal of mathematics, 3(1) (2008), 14-22.
[11] G.N. Arzhantseva
and I.G. Lysenok,
A
lower bound on the growth of word hyperbolic groups,
Journal of the
London Mathematical Society, (2) 73 (2006),
109-125. abs
pdf
2
citations by
J. Button, Non proper HNN extensions and uniform uniform exponential growth, (2009), arXiv.org:0909.2841
F. Zuddas, Some finiteness results for groups with bounded algebraic entropy, Geom. Dedicata (2009), 49-62.
[12] G.N. Arzhantseva,
V.S. Guba,
L.Guyot,
Growth
rates of amenable groups,
Journal of Group Theory, 8
(2005), no.3, 389-394.
abs
ps
1
citation by
V. Guba, Strict dead-end elements in free soluble groups, Comm. Algebra 36 (2008), no. 5, 1988-1997. MR2424281 (2009d:20074)
[13] G.N. Arzhantseva,
J. Burillo,
M. Lustig,
L. Reeves, H.
Short, E. Ventura, Uniform
non-amenability,
Advances in
Mathematics, 197 (2005), no. 2, 499-522.
abs
intro
pdf
18
citations by
J. Anderson, J. Aramayona, K.J. Shackleton, Uniformly exponential growth and mapping class groups of surfaces, In the tradition of Ahlfors-Bers. IV, 1-6,
Contemp.
Math., 432, Amer. Math. Soc.,
V. Atabekyan, Uniform nonamenability of subgroups of free Burnside groups of odd period, Math. Notes, 85 (4) (2009), 496-502.
J. Bannon, M. Ravichandran, A Følner invariant for type II1 factors, Expo. Math. 25 (2007), no. 2, 117-130. MR2319573 (2008c:46090)
E. Breuillard, T. Gelander, Uniform independence in linear groups, Invent. Math. 173 (2008), no. 2, 225-263. MR2415307 (2009j:20068)
E. Breuillard, T. Gelander, Cheeger constant and algebraic entropy of linear groups, Int. Math. Res. Not. (2005), no. 56, 3511-3523. MR2200587 (2006m:20061)
J. Burillo, Grups paradoxa de Banach Tarski, Butlletí de la Societat Catalana de Matemàtiques,Vol. 23, núm. 2, 2008. Pàg. 181-199.
Y. de Cornulier, L. Guyot, W. Pitsch, On the isolated points in the space of groups, J. Algebra 307 (2007), no. 1, 254-277. MR2278053 (2008c:20082)
Y. de Cornulier, L. Guyot. W. Pitsch, The space of subgroups of an abelian group, (2008), arXiv.org:0811.1549
M. Ershov, A. Jaikin-Zapirain, Kazhdan quotients of Golod-Shafarevich groups, (2009), arXiv:org:0908.3734
L. Guyot, Y. Stalder, Limits of Baumslag-Solitar groups and dimension estimates in the space of marked groups, 2010, arXiv:1001.5371
R. Lyons, M. Pichot, S. Vassout, Uniform non-amenability, cost, and the first l2-Betti number, Groups Geom. Dyn. 2 (2008), no. 4, 595-617. MR2442947 (2009i:20080)
P. Nowak, Isoperimetry of group actions, Adv. Math. 219 (2008), no. 1, 1-26. MR2435418 (2009g:20097)
A.Yu. Olshanskii, M.V. Sapir, On k-free-like groups, Algebra and Logic 48 (2) (2009), 245-257.
D. Osin,
Uniform non-amenability of
free Burnside groups, Arch.
Math. (
D. Osin, L2-Betti numbers and non-unitarizable groups without free subgroups, Int. Math. Res. Not. IMRN2009, no. 22, 4220-4231. MR2552302 (2010k:22007)
M. Pichot, Semi-continuity of the first l2-Betti number on the space of finitely generated groups, Comment. Math. Helv. 81 (2006), no. 3, 643-652. MR2250857 (2007e:20089)
Y. Stalder, Convergence of Baumslag-Solitar groups, Bull. Belg. Math. Soc. Simon Stevin 13 (2006), no. 2, 221-233. MR2259902 (2008f:20047)
R. Willett, Property A and graphs with large girth, (2011), preprint.
[14]
G.N. Arzhantseva
and P.-A. Cherix, On
the Cayley
graph of a generic
finitely presented group,
Bulletin of the
Belgian Mathematical Society, 11 (2004), no. 4,
589-601. abs
intro
ps
4
citations by
T. G. Ceccherini-Silberstein, A. Y. Samet-Vaillant, Asymptotic invariants of finitely generated algebras. A generalization of Gromov's quasi-isometric viewpoint, Journal of Mathematical Sciences, 156 (1) (2009), 56-108.
I. Kapovich, P. Schupp, On group-theoretic models of randomness and genericity, Groups Geom. Dyn. 2 (2008), no. 3, 383-404. MR2415305 (2009k:20102)
Y. Ollivier,
A
January 2005 invitation to random groups,
Ensaios
Matemáticos,
10. Sociedade
Brasileira
de Matemática,
Y. Ollivier, Sharp phase transition theorems for hyperbolicity, Geom. Funct. Anal. 14 (2004), no. 3, 595—679. MR2100673 (2005m:20101)
[15] G.N. Arzhantseva
and I.G. Lysenok,
Growth tightness for word
hyperbolic groups,
Mathematische
Zeitschrift,
241 (2002), no. 3, 597--611. abs
intro
pdf
14
citations by
L. Bartholdi,
R. Grigorchuk,
V. Nekrashevych,
From fractal groups to fractal
sets,
Fractals in Graz 2001, 25-118,
Trends Math., Birkhäuser,
Basel, 2003.
MR2091700 (2005h:20056)
T. Ceccherini-Silberstein, F. Scarabotti, Random walks, entropy and hopfianity of free groups, Random walks and geometry, 413-419, Walter de Gruyter GmbH & Co. KG, Berlin, 2004. MR2087792 (2005h:60131)
T. Ceccherini-Silberstein, W. Woess, Growth and ergodicity of context-free languages, Trans. Amer. Math. Soc. 354 (2002), no. 11, 4597-4625. MR1926891 (2003g:68067)
F. Dal’bo, M. Peigné, J.-C. Picaud, A. Sambusetti, On the growth of quotients of Kleinian groups, Ergod. Th. & Dynam. Sys. (2010), published online.
A. Erschler, Growth rates of small cancellation groups, Random walks and geometry, 421-430, Walter de Gruyter GmbH & Co. KG, Berlin, 2004. MR2087793 (2005f:20061)
P. de la Harpe, Uniform growth in groups of exponential growth, Geom. Dedicata 95 (2002), 1-17. MR1950882 (2003k:20031)
P. de la Harpe, Topics
in geometric group theory,
Chicago Lectures in Mathematics.
W. Huss, E. Sava, W. Woess, Entropy sensitivity of languages defined by infinite automata, via Markov chains with forbidden transitions, Theoretical Computer Science, 2010, to appear, arXiv:0911.0142
Y. Ollivier,
A
January 2005 invitation to random groups,
Ensaios
Matemáticos,
10. Sociedade
Brasileira
de Matemática,
Y. Ollivier, Growth exponent of generic groups, Comment. Math. Helv. 81 (2006), no. 3, 569-593. MR2250854 (2007d:20120)
A. Sambusetti, Asymptotic properties of coverings in negative curvature, Geom. Topol. 12 (2008), no. 1, 617-637. MR90354 (2009g:53058)
A. Sambusetti, Growth tightness of negatively curved manifolds, C. R. Math. Acad. Sci. Paris 336 (2003), no. 6, 487-491. MR1975085 (2004a:53048)
A. Sambusetti, Growth tightness of surface groups, Expo. Math. 20 (2002), no. 4, 345-363. MR1940012 (2003k:57004)
A. Talambutsa, Attainability of the index of exponential growth in free products of cyclic groups, Math. Notes 78 (2005), no. 3-4, 569-572. MR2226734 (2007a:20028)
[16] G.N. Arzhantseva
and D.V. Osin,
Solvable groups with polynomial
Dehn
functions,
Transactions of the
American Mathematical Society, 354 (2002),
3329-3348. abs
intro
pdf
9
citations by
D. Kahrobaei, M. Anshel, Decision and Search in Non-Abelian Cramer-Shoup Public Key Cryptosystem, Groups Complex. Cryptol. 1, (2009) no. 2, 217-225.
N. Broaddus, B. Farb, A. Putman, Irreducible Sp-representations and subgroup distortion in the mapping class group, (2007), arXiv.org:0707.2262
Y. de
Cornulier,
R. Tessera, Metabelian groups with
quadratic Dehn
function and Baumslag-Solitar
groups, (2010),
arXiv:1003.0148
C. Drutu, Filling
in solvable
groups and in lattices in semisimple
groups,
Topology 43 (2004), no. 5, 983-1033. MR2079992 (2005h:20078)
P. Davidson, Geometric methods in the study of Pride groups and relative presentations, (2008), PhD thesis, University of Glasgow. http://theses.gla.ac.uk/230/01/2008davidsonphd.pdf
W. Dison, T.R. Riley, Hydra groups, (2010), arXiv:1002.1945
R.
Ji, C.
Ogle,
B. Ramsey, B-Bounded
cohomology
and applications,
arXiv:1004.4677
M. Kassabov,
T. Riley,
The
Dehn function of Baumslag's metabelian
group (2010), arXiv:1008.1966
E. Leuzinger,
Geometriae
Dedicata,
87 (2001), 191-208. abs
intro
pdf
13
citations by
T. Delzant, M. Gromov, Cuts in Kähler groups, Infinite groups: geometric, combinatorial and dynamical aspects, 31-55,
Progr.
Math.,
248, Birkhäuser,
B. Farb, L. Mosher, Convex cocompact subgroups of mapping class groups, Geom. Topol. 6 (2002), 91-152 (electronic). MR1914566 (2003i:20069)
Y. Glasner,
J. Souto,
P. Storm,
P. de la Harpe, Topics
in geometric group theory,
Chicago Lectures in Mathematics.
E. Jabara, Groups that are the union of a finite number of double cosets, Rend. Sem. Mat. Univ. Padova 116 (2006), 41-53. MR2287342 (2008c:20056)
I. Kapovich, R. Weidmann, Kleinian groups and the rank problem, Geom. Topol. 9 (2005), 375-402. MR2140986 (2006d:20079)
I. Kapovich, The Frattini subgroups of subgroups of hyperbolic groups, J. Group Theory 6 (2003), no. 1, 115-126. MR1953799 (2003j:20075)
I. Kapovich, The non-amenability of Schreier graphs for infinite index quasiconvex subgroups of hyperbolic groups, Enseign. Math. (2) 48 (2002), no. 3-4, 359-375. MR1955607 (2003j:20074)
I. Kapovich, The geometry of relative Cayley graphs for subgroups of hyperbolic groups, (2002), arXiv:math/0201045
E. Martínez-Pedroza, Combination of quasiconvex subgroups of relatively hyperbolic groups, Groups Geom. Dyn. 3 (2009), no. 2, 317-342. MR2486802
A. Minasyan, Some properties of subsets of hyperbolic groups, Comm. Algebra 33 (2005), no. 3, 909-935. MR2128420 (2006c:20088)
A. Minasyan, On products of quasiconvex subgroups in hyperbolic groups, Internat. J. Algebra Comput. 14 (2004), no. 2, 173-195. MR2058319 (2005a:20063)
A. Minasyan, On quasiconvex subsets of hyperbolic groups, (2005), PhD thesis, Vanderbilt University.
[18] G.N. Arzhantseva,
A property of
subgroups of infinite index in a free group,
Proceedings of the
American Mathematical Society, 128 (11) (2000),
3205-3210.
abs
intro
pdf
19
citations by
F. Bassino, A. Martino, C. Nicaud, E. Ventura, P. Weil, Statistical properties of subgroups of free groups, (2010), arXiv:1001.4472v1
A.V. Borovik, A.G. Myasnikov, V.N. Remeslennikov, Generic complexity of the conjugacy problem in HNN-extensions and algorithmic stratification of Miller's groups, Internat. J. Algebra Comput. 17 (2007), no. 5-6, 963-997. MR2355678 (2008m:20046)
A.V. Borovik, A.G. Myasnikov, V.N. Remeslennikov, Multiplicative measures on free groups, Internat. J. Algebra Comput. 13 (2003), no. 6, 705-731. MR2028100 (2004k:20051)
A. Borovik,
A.G. Myasnikov,
V. Shpilrain,
Measuring sets in infinite
groups,
Computational and statistical group theory (Las Vegas, NV/Hoboken, NJ,
2001),
21-42, Contemp.
Math., 298, Amer. Math. Soc.,
L. Ciobanu,
A. Martino,
J. Friedman, The Strengthened Hanna Neumann Conjecture I: A Combinatorial Proof, (2010), arXiv:1003.5739v3
V. Kaimanovich, I. Kapovich, P. Schupp, The subadditive ergodic theorem and generic stretching factors for free group automorphisms, Israel J. Math. 157 (2007), 1-46. MR2342439 (2009d:20099)
I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Average-case complexity and decision problems in group theory, Adv. Math. 190 (2005), no. 2, 343-359. MR2102661 (2005i:20053)
I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Generic-case complexity, decision problems in group theory, and random walks, J. Algebra 264 (2003), no. 2, 665-694. MR1981427 (2005m:20080)
I. Kapovich, P. Schupp, Random quotients of the modular group are rigid and essentially incompressible, J. Reine Angew. Math. 628 (2009), 91-119. MR2503236
I. Kapovich, P. Schupp, On group-theoretic models of randomness and genericity, Groups Geom. Dyn. 2 (2008), no. 3, 383-404. MR2415305 (2009k:20102)
I. Kapovich, P. Schupp, V. Shpilrain, Generic properties of Whitehead's algorithm and isomorphism rigidity of random one-relator groups, Pacific J. Math. 223 (2006), no. 1, 113-140. MR2221020 (2007e:20068)
I. Kapovich, P. Schupp, Delzant's T-invariant, Kolmogorov complexity and one-relator groups, Comment. Math. Helv. 80 (2005), no. 4, 911-933. MR2182705 (2007d:20062)
I. Kapovich, P. Schupp, Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups, Math. Ann. 331 (2005), no. 1, 1-19. MR2107437 (2005h:20079)
I. Kapovich, P. Schupp, Bounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion, Proc. London Math. Soc. (3) 88 (2004), no. 1, 89-113. MR2018959 (2005a:20061)
S. Margolis,
J. Meakin,
Z. Sunik,
Distortion functions and the
membership problem
for submonoids
of groups and monoids,
Geometric methods in group theory, 109-129, Contemp.
Math., 372, Amer. Math. Soc.,
Y. Ollivier,
A
January 2005 invitation to random groups,
Ensaios
Matemáticos, 10. Sociedade
Brasileira
de Matemática,
M. Sapir, Asymptotic invariants, complexity of groups and related problems, (2010), arXiv:1012.1325
B. Solie, Genericity of filling elements, (2010), arXiv:1007.4022
[19] G.N. Arzhantseva,
Generic
properties of finitely presented groups and Howson's
Theorem,
Communications in
Algebra, 26 (11) (1998), 3783-3792.
mathscinet
intro
24
citations by
T. G. Ceccherini-Silberstein, A. Y. Samet-Vaillant, Asymptotic invariants of finitely generated algebras. A generalization of Gromov's quasi-isometric viewpoint, Journal of Mathematical Sciences, 156 (1) (2009), 56-108.
B. Fine, A. Myasnikov, G. Rosenberger, Generic subgroups of group amalgams, Groups Complex. Cryptol. 1 (2009), no. 1, 51-61. MR2502936
E. Frenkel, A.G. Myasnikov, V.N. Remeslennikov, Regular sets and counting in free groups, (2009), arXiv:0906.2850
R.
Gilman, A. Miasnikov, D. Osin, Exponentially
generic subsets of
groups, (2010),
arXiv:1007.0552v1
E. Ghys, Random groups (following Misha Gromov, ...), Astérisque No. 294 (2004), viii, 173-204. MR2111644 (2005j:20049)
P. de la Harpe, Topics
in geometric group theory,
Chicago Lectures in Mathematics.
V. Kaimanovich, I. Kapovich, P. Schupp, The subadditive ergodic theorem and generic stretching factors for free group automorphisms, Israel J. Math. 157 (2007), 1-46. MR2342439 (2009d:20099)
I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Average-case complexity and decision problems in group theory, Adv. Math. 190 (2005), no. 2, 343-359. MR2102661 (2005i:20053)
I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Generic-case complexity, decision problems in group theory, and random walks, J. Algebra 264 (2003), no. 2, 665-694. MR1981427 (2005m:20080)
I. Kapovich, I. Rivin, P. Schupp, V. Shpilrain, Densities in free groups and Zk, visible points and test elements, Math. Res. Lett. 14 (2007), no. 2, 263-284.
I. Kapovich, P. Schupp, Delzant's T-invariant, Kolmogorov complexity and one-relator groups, Comment. Math. Helv. 80 (2005), no. 4, 911-933. MR2182705 (2007d:20062)
I. Kapovich, P. Schupp, Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups, Math. Ann. 331 (2005), no. 1, 1-19. MR2107437 (2005h:20079)
I. Kapovich, P. Schupp, On group-theoretic models of randomness and genericity, Groups Geom. Dyn. 2 (2008), no. 3, 383-404. MR2415305 (2009k:20102)
I. Kapovich, P. Schupp, Random quotients of the modular group are rigid and essentially incompressible, J. Reine Angew. Math. 628 (2009), 91-119. MR2503236
I. Kapovich, P. Schupp, Bounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion, Proc. London Math. Soc. (3) 88 (2004), no. 1, 89-113. MR2018959 (2005a:20061)
I. Kapovich, P. Schupp, V. Shpilrain, Generic properties of Whitehead's algorithm and isomorphism rigidity of random one-relator groups, Pacific J. Math. 223 (2006), no. 1, 113-140. MR2221020 (2007e:20068)
I. Kapovich, R. Weidmann, Freely indecomposable groups acting on hyperbolic spaces, Internat. J. Algebra Comput. 14 (2004), no. 2, 115-171. MR2058318 (2005f:20079)
M. Lustig, Y. Moria, Horizontal Dehn surgery and genericity in the curve complex, (2007), arXiv:0711.4492v4
Y. Ollivier, Sharp phase transition theorems for hyperbolicity, Geom. Funct. Anal. 14 (2004), no. 3, 595-679. MR2100673 (2005m:20101)
Y. Ollivier,
A
January 2005 invitation to random groups,
Ensaios
Matemáticos,
10. Sociedade
Brasileira
de Matemática,
Y. Ollivier, Critical densities for random quotients of hyperbolic groups, C. R. Math. Acad. Sci. Paris 336 (2003), no. 5, 391-394.
M.
Sapir, Asymptotic
invariants, complexity of groups and related problems,
(2010), arXiv:1012.1325.
B.
Solie,
Genericity
of filling elements,
(2010), arXiv:1007.4022
[20] G.N.Arzhantseva,
On groups
in which subgroups with a fixed number of generators are free,
Fundamental and
Applied Mathematics,
3(3)
(1997), 675-683 (in Russian). abs
18
citations by
Yu. Bahturin, A. Olshanskii, Actions of maximal growth, Proc. London Math. Soc. (2010) 101(1): 27-72
I. Bumagin, On small cancellation k-generated groups with (k-1)-generated subgroups all free, Internat. J. Algebra Comput. 11 (2001), no. 5, 507-524. MR1869228 (2003a:20052)
S. Cleary, M. Elder, A. Rechnitzer, J. Taback, Random subgroups of Thompson's group F, (2007), arXiv:0711.1343
E. Frenkel, A.G. Myasnikov, V.N. Remeslennikov, Regular sets and counting in free groups, (2009), arXiv:0906.2850
R. Gilman, A. Miasnikov, D. Osin, Exponentially generic subsets of groups, (2010), arXiv:1007.0552v1
E. Ghys, Random groups (following Misha Gromov, ...), Astérisque No. 294 (2004), viii, 173-204. MR2111644 (2005j:20049)
V. Kaimanovich, I. Kapovich, P. Schupp, The subadditive ergodic theorem and generic stretching factors for free group automorphisms, Israel J. Math. 157 (2007), 1-46. MR2342439 (2009d:20099)
I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Average-case complexity and decision problems in group theory, Adv. Math. 190 (2005), no. 2, 343-359. MR2102661 (2005i:20053)
I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Generic-case complexity, decision problems in group theory, and random walks, J. Algebra 264 (2003), no. 2, 665-694. MR1981427 (2005m:20080)
I. Kapovich, I. Rivin, P. Schupp, V. Shpilrain, Densities in free groups and Zk, visible points and test elements, Math. Res. Lett. 14 (2007), no. 2, 263-284.
I. Kapovich, P. Schupp, Random quotients of the modular group are rigid and essentially incompressible, J. Reine Angew. Math. 628 (2009), 91-119. MR2503236
I. Kapovich, P. Schupp, On group-theoretic models of randomness and genericity, Groups Geom. Dyn. 2 (2008), no. 3, 383-404. MR2415305 (2009k:20102)
I. Kapovich, P. Schupp, Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups, Math. Ann. 331 (2005), no. 1, 1-19. MR2107437 (2005h:20079)
I. Kapovich, P. Schupp, Delzant's T-invariant, Kolmogorov complexity and one-relator groups, Comment. Math. Helv. 80 (2005), no. 4, 911-933. MR2182705 (2007d:20062)
I. Kapovich, P. Schupp, Bounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion, Proc. London Math. Soc. (3) 88 (2004), no. 1, 89-113. MR2018959 (2005a:20061)
I. Kapovich, P. Schupp, V. Shpilrain, Generic properties of Whitehead's algorithm and isomorphism rigidity of random one-relator groups, Pacific J. Math. 223 (2006), no. 1, 113-140. MR2221020 (2007e:20068)
Y. Ollivier,
A
January 2005 invitation to random groups,
Ensaios
Matemáticos,
10. Sociedade
Brasileira
de Matemática,
M. Sapir, Asymptotic invariants, complexity of groups and related problems, (2010), arXiv:1012.1325.
[21] G.N. Arzhantseva
and A.Yu.
Ol'shanskii,
Generality of the class of
groups in which subgroups
with
a lesser number of generators are free,
Mathematical Notes, 59(3-4)
(1996), 350-355. mathscinet pdf
28
citations by
S. Cleary, M. Elder, A. Rechnitzer, J. Taback, Random subgroups of Thompson's group F, (2007), arXiv:0711.1343
E. Frenkel, A.G. Myasnikov, V.N. Remeslennikov, Regular sets and counting in free groups, (2009), arXiv:0906.2850
E. Ghys, Random groups (following Misha Gromov, ...), Astérisque No. 294 (2004), viii, 173-204. MR2111644 (2005j:20049)
L. Guyot, Estimating Minkowski dimensions in the space of marked groups, Ann. Fac. Sci. Toulouse Math. (6) 16 (2007), no. 1, 107-124. MR2325594 (2008e:20063)
P. de la Harpe, Uniform growth in groups of exponential growth, Geom. Dedicata 95 (2002), 1-17. MR1950882 (2003k:20031)
V. Kaimanovich, I. Kapovich, P. Schupp, The subadditive ergodic theorem and generic stretching factors for free group automorphisms, Israel J. Math. 157 (2007), 1-46. MR2342439 (2009d:20099)
I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Average-case complexity and decision problems in group theory, Adv. Math. 190 (2005), no. 2, 343-359. MR2102661 (2005i:20053)
I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Generic-case complexity, decision problems in group theory, and random walks, J. Algebra 264 (2003), no. 2, 665-694. MR1981427 (2005m:20080)
I. Kapovich, I. Rivin, P. Schupp, V. Shpilrain, Densities in free groups and Zk, visible points and test elements, Math. Res. Lett. 14 (2007), no. 2, 263-284.
I. Kapovich, P. Schupp, Random quotients of the modular group are rigid and essentially incompressible, J. Reine Angew. Math. 628 (2009), 91-119. MR2503236
I. Kapovich, P. Schupp, On group-theoretic models of randomness and genericity, Groups Geom. Dyn. 2 (2008), no. 3, 383-404. MR2415305 (2009k:20102)
I. Kapovich, P. Schupp, Delzant's T-invariant, Kolmogorov complexity and one-relator groups, Comment. Math. Helv. 80 (2005), no. 4, 911-933. MR2182705 (2007d:20062)
I. Kapovich, P. Schupp, Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups, Math. Ann. 331 (2005), no. 1, 1-19. MR2107437 (2005h:20079)
I. Kapovich, P. Schupp, Bounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion, Proc. London Math. Soc. (3) 88 (2004), no. 1, 89-113. MR2018959 (2005a:20061)
I. Kapovich, P. Schupp, V. Shpilrain, Generic properties of Whitehead's algorithm and isomorphism rigidity of random one-relator groups, Pacific J. Math. 223 (2006), no. 1, 113-140. MR2221020 (2007e:20068)
I. Kapovich, R. Weidmann, Kleinian groups and the rank problem, Geom. Topol. 9 (2005), 375-402. MR2140986 (2006d:20079)
I. Kapovich, R. Weidmann, Freely indecomposable groups acting on hyperbolic spaces, Internat. J. Algebra Comput. 14 (2004), no. 2, 115-171. MR2058318 (2005f:20079)
I. Kozakov,
Percolation and Ising
model on graphs with tree-like structure,
(2008),
PhD thesis,
S. Margolis,
J. Meakin,
Z. Sunik,
Distortion functions and the
membership problem
for submonoids
of groups and monoids,
Geometric methods in group theory, 109-129, Contemp.
Math., 372, Amer. Math. Soc.,
L. Markus-Epstein, Stallings foldings and subgroups of amalgams of finite groups, Internat. J. Algebra Comput. 17 (2007), no. 8, 1493-1535. MR2378049 (2009c:20044)
A. Myasnikov, V. Shpilrain, A. Ushakov, Group-based cryptography, Birkhäuser, 2008.
Y. Ollivier, Sharp phase transition theorems for hyperbolicity, Geom. Funct. Anal. 14 (2004), no. 3, 595-679. MR2100673 (2005m:20101)
Y. Ollivier, Critical densities for random quotients of hyperbolic groups, C. R. Math. Acad. Sci. Paris 336 (2003), no. 5, 391-394.
Y. Ollivier,
A
January 2005 invitation to random groups,
Ensaios
Matemáticos,
10. Sociedade
Brasileira
de Matemática,
M. Sapir, Asymptotic invariants, complexity of groups and related problems, (2010), arXiv:1012.1325.
P. Schupp, Coxeter groups, 2-completion, perimeter reduction and subgroup separability, Geom. Dedicata 96 (2003), 179-198. MR1956839 (2003m:20052)
D.T. Wise, Sectional curvature, compact cores, and local quasiconvexity, Geom. Funct. Anal. 14 (2004), no. 2, 433-468. MR2062762 (2005i:53043)
[22] G.N. Arzhantseva,
Generic
properties of finitely presented groups,
PhD thesis,
Books
(edited):
[23]
G.N. Arzhantseva,
A.Valette
(eds.), Limits of graphs in
group theory and
computer science,
Fundamental Sciences, EPFL
Press, Lausanne, 2009, 305 pp. book
[24] G.N. Arzhantseva,
L. Bartholdi, J. Burillo,
and E. Ventura (eds.), Geometric
group theory,
Trends in Mathematics, Birkhäuser
Verlag,
Basel, 2007, 253 pp. book
Submitted
papers and preprints:
[25] G.N. Arzhantseva, J.-F.
Lafont, A. Minasyan, Isomorphism versus
commensuarability for a class of finitely presented groups,
(2011).
pdf
NEW
!
[26] G.N. Arzhantseva, E.
Guentner, J. Spakula, Coarse
non-amenability and coarse embeddings,
(2011), submitted. pdf NEW
!
2 citations by
R. Willett, Property A and graphs with large girth, (2011), preprint.
M. Ostrovskii, Low-distortion embeddings of graphs with large girth, (2011), arxiv.org:1108.2542
[27] G.N.
Arzhantseva
and T. Delzant,
Examples of random groups, Journal of Topology (2008),
submitted:
first version (October 28, 2008), revised version (August 26,
2011). pdf
16 citations by
A. Bartels, W. Luck, The Borel conjecture for hyperbolic and CAT(0)-groups, (2009), arXiv.org:0901.0442
Y. de Cornulier, Y. Stalder, A. Valette, Proper actions of wreath products and generalizations, (2009), arxiv.org:0905.3960
R. Coulon, Asphericity and small cancellation theory for rotation family of groups, (2009), arxiv:0907.4577
R. Coulon, Automorphismes extérieurs du groupe de Burnside libre, PhD thesis, University of Strasbourg, 2010.
E.
Guentner,
R. Tessera, G. Yu, A
notion of geometric complexity and its application to topological
rigidity, arxiv:1008.0884v1
V. Lafforgue, Conjecture
de Baum-Connes, théorie de Fonataine en
caractéristique p, et programme de
Langlands géométriques,
(2009), Habilitation thesis,
University of Paris 7.
W. Lueck, Survey on aspherical manifolds, (2009), arXiv:0902.2480v3
W. Lueck, K- and L-theory of group rings, (2010), arXiv:1003.5002v1
A. Naor, L. Silberman, Poincaré inequalities, embeddings, and wild groups,(2010), arXiv:1005.4084
P. Nowak, G. Yu, Large-Scale geometry, (2010), EMS publishing house, to appear. http://www.math.tamu.edu/~pnowak/book_etb/book_etb.pdf
M. Sapir, Asymptotic
invariants, complexity of groups and related problems,
(2010), arXiv:1012.1325
M. Sapir, Aspherical groups and
manifolds with extreme properties,
(2011), arXiv:1103.3873
J. Spakula, R. Willett, On rigidity
of Roe algebras,
(2011), preprint.
R. Willett, Property A and graphs with large girth,
(2011), preprint.
R. Willett, G. Yu, Higher index theory for certain expanders
and Gromov monster groups I,
(2011), arXiv:1012.4150
R. Willett, G. Yu, Higher index theory
for certain expanders and Gromov monster groups II, (2011), arXiv:1012.4151
[28] G.N. Arzhantseva,
An algorithm detecting Dehn
presentations,
preprint,
1
citation by
V. Diekert, A. Duncan, A. Myasnikov, Geodesic rewriting systems and pregroups, (2009), arXiv.org:0906.2223
Papers in Theoretical Computer Science/Applied mathematics (refereed):
[29] G.N. Arzhantseva,
J. Díaz,
J. Petit, J.D.P. Rolim,
and
M. Serna, Broadcasting on
networks of sensors
communicating
through directional antennas,
Ambient Intelligence
Computing,
1-12, Proceedings, CTI Press
and Ellinika
Grammata,
2003. abs
ps
[30] G.N. Arzhantseva
and J.D.P. Rolim,
Considerations for a geometric
model of the web,
Approximation
and Randomization Algorithms
in Communication Networks, Rome, 2002,
1-11, Proceedings, Carleton
Scientific. abs
[31] G.N. Arzhantseva
and J.D.P. Rolim,
Computability and Complexity,
e-learning theoretical
course of the Virtual Logic Laboratory
(a project of the Swiss
Virtual Campus),
90 pp. (electronic tutorial). abs
Papers in preparation:
G.N.
Arzhantseva
and M. Lustig,
A first course in geometric
group
theory, graduate textbook
project.
G.N.
Arzhantseva,
Geometry of small cancellation
and Burnside factors, lecture
notes of
the Borel
seminar minicourse.
G.
N. Arzhantseva,
Infinite groups: Growth and Isoperimetry,
lecture notes, the IIIe
Cycle Romand
de mathématiques.
Conference announcements:
G.N. Arzhantseva,
Genericity
of Howson's
property of finitely presented
groups,
International Algebraic
Conference dedicated to the memory of D.K.
Faddeev,
Saint-Petersburg, Russia, 24-30 June, 1997.
Abstracts, 158-159.
G.N.
Arzhantseva,
Generic classes of finitely
presented
groups,
International Conference
"Modern problems of Number Theory and
Applications",
G.N.
Arzhantseva,
Generic classes of finitely
presented
groups,
International Conference
"Mathematics. Modeling.
Ecology"