Algebra/Topology Seminar

Speaker: Zhengfang Wang

Title: Goresky-Hingston product via (singular) Hochschild cohomology

Abstract: The singular Hochschild cohomology (also called Tate-Hochschild cohomology) is defined as the graded endomorphisms of the diagonal bimodule in the singularity category (in the sense of Buchweitz and Orlov) of bimodules.

In this talk, we will show how the singular Hochschild cohomology of (dg) Frobenius algebras naturally recovers the Goresky-Hingston product in string topology for the simply connected case. This is joint work with M. Rivera. We will also explain how to deal with the non-simply connected case using Hochschild cohomology of generalised cluster category, based on joint work in progress with M. Rivera and A. Takeda.