Speaker: Lukas Müller (Heriot-Watt University)
Title: Equivariant Topological Field Theories and Homotopy Theory
Abstract: Equivariant topological field theories, introduced by Turaev, are a type of topological field theory defined on manifolds equipped with principal $G$-bundles. They are related to $G$-graded algebraic structures such as $G$-crossed Frobenius algebras and $G$-crossed categories. Via an orbifold construction they give rise to topological quantum field theories.
In my talk I will extend the notion of an equivariant topological field theory using technics from homotopy theory. In this framework the genus zero part of two-dimensional equivariant topological field theory is captured by a topological operad called the little bundles operad. Furthermore, I will explain how an equivariant version of higher derived Hochschild chains provides an example of an equivariant topological field theory.
The talk is based on joint work with Lukas Woike.