Orateur: Paolo
Aceto (Alfréd Rényi Institute of Mathematics)
Titre: Knot concordance
and homology sphere groups
Résumé:
I will discuss properties of two homomorphisms to the rational
homology sphere group.
The first one, induced by the inclusion, is a homomorphism from the
integral homology sphere group. Using work of Lisca I will show that the
image of this map intersects trivially with the subgroup of the rational
homology sphere group generated by lens spaces. As corollaries this gives a
new proof that the cokernel is infinitely generated, and implies that a
connected sum $K$ of 2-bridge knots is concordant to a knot with determinant
1 if and only if $K$ is smoothly slice.
The second map is the homomorphism from the knot concordance group defined
by taking double branched covers of knots. Here it is possible to prove that
the kernel contains a free infinitely generated summand by analyzing the
Tristram-Levine signatures of a family of knots whose double branched covers
all bound rational homology balls. This is joint work with Kyle Larson.