Orateur: Krzysztof
Putyra (EPFZ)
Titre: Quantum Link
Homology via Trace Functor.
Résumé:
Trace functors are algebraic analogues of gluing together components
of the boundary a of manifold. In particular, one can produce a TQFT functor
for cobordisms embedded into a surface bundle M with fiber F from an
extended TQFT for cobordisms with corners in F x I. In my talk I will
discuss an application of this construction to link homology. Chen and
Khovanov assigned a chain complex to a tangle in a thickened plane, and we
have shown that Hochschild homology of this chain complex recovers the
Asaesa-Przytycki-Sikora invariant for links in a thickened annulus. I will
describe how to deform the Hochschild homology to obtain a richer invariant,
which we call the quantum link homology. This new homology admits an action
of the quantum group Uq(sl_2) and is projectively functorial with respect to
link cobordisms, leading to invariants of knotted surfaces in 4D. We provide
evidence that this invariant is non-trivial. This is a joint work with Anna
Beliakova (University of Zurich) and Stephan Wehrli (Syracuse University).
Reference: arXiv:1605.03523