## Topology and Geometric Group Theory Seminar

Foling ZouUniversity of Michigan
Equivariant factorization homology of Thom spectra
Tuesday, February 9, 2021 - 1:30pm
Via Zoom

This is joint work with Asaf Horev and Inbar Klang. Factorization homology theories are invariants of n-manifolds with coefficients in suitable E_n-algebras. Let G be a finite group and V be a finite dimensional G-representation. The equivariant factorization homology for V-framed G-manifolds have E_V-algebra as coefficients. We show that when coefficient algebra A is the Thom spectrum of an E_{V+W}-map for a large enough representation W, the factorization homology of A can be computed by a certain Thom spectrum. With nonabelian Poincare duality theorem, we are able to simplify the result in some cases. In particular, we compute THR(HF_2), THR(HZ_(2)), THH_{C_2}(HF_2).

There will be a pretalk by J. D. Quigley at 1pm.