Algebraic Topology Seminar

The factorization homology are invariants of $n$-dimensional manifolds with some fixed tangential structures that take coefficients in suitable $E_n$-algebras. In this talk, I will discuss the equivariant factorization homology of framed $G$-manifolds for a finite group $G$. These manifolds are $V$-framed for a $G$-representation $V$, and the coefficients for the theory are $E_V$-spaces or $E_V$-spectra. I will prove the equivariant nonabelian Poincare duality theorem in this case. As an application, in joint work with Asaf Horev and Inbar Klang, we compute the equivariant factorization homology on equivariant spheres for certain Thom spectra. Speaker(s): Foling Zou (University of Michigan)