##### Department of Mathematics,

University of California San Diego

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### Math 292 - Topology Seminar

## Foling Zou

#### University of Michigan

## Equivariant nonabelian Poincar\'e duality and equivariant factorization homology of Thom spectra

##### Abstract:

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 Poincar\'e duality theorem, we are able to simplify the result in some cases. In particular, we compute $\mathrm{THR}(\mathrm{H}\mathbb{F}_{2})$, $\mathrm{THR}(\mathrm{H}\mathbb{Z}_{(2)})$, $\mathrm{THH}_{C_2}(\mathrm{H}\mathbb{F}_2)$.

Host: Zhouli Xu

### January 19, 2021

### 10:30 AM

### Zoom information: Meeting ID: 933 6734 4286 Password: topology

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