GP Seminar: Partially defined TQFTs and Y-infinity algebras

Abstract: There is a functorial perspective on TQFTs known generally by the name of the ‘cobordism hypothesis’, which encodes the data of such a topological theory in terms of a functor out of a category of bordisms, or equivalently a certain type of object in the target category. I will explain some of this perspective, and then talk about a relaxation of this definition, where the resulting theory is only defined on a certain class of bordisms. I will explain one such example, partially defined oriented 2d TQFTs, and show how the resulting algebraic structure in many cases can be described by a type of properadic algebra we call Y-infinity algebra. This talk is about joint papers with M. Kontsevich and Y. Vlassopoulos, together with more recent ongoing work with C. Emprin.

This is a seminar in the Centre of Geometry and Physics seminar series.