Two-dimensional Extended HQFTs

Topological quantum field theories (TQFTs), inspired by theoretical physics, produce manifold invariants behaving well under gluing. For every discrete group G, homotopy quantum field theories (HQFTs) are G-equivariant versions of TQFTs. In this talk, we define and classify 2-dimensional extended HQFTs generalizing methods introduced for TQFTs by Chris Schommer-Pries in 2009. We list generators and relations for the extended G-equivariant bordism bicategory and use them to classify 2-dimensional extended HQFTs.