Fully local equivariant field theories

Topological field theories (TFTs) provide local invariants of manifolds in the sense that these can be computed by decompositions. It is possible to consider versions of TFTs where all manifolds are equipped with additional topological structures such as a map into a fixed topological space. Equivariant TFTs, defined by Turaev, correspond to the case where all manifolds are oriented and equipped with a map into the classifying space of a finite group BG.

In my talk I will introduce all these concepts in more detail and allude to the mathematics going into precise definitions and classification results. I will also discuss sources of examples coming from local to global constructions. The talk is mostly based on joint work with Lukas Woike. I will also briefly talk about joint work in progress with Corina Keller.