Equivariant nonabelian Poincaré duality and equivariant factorization homology of Thom spectra

Abstract

In this paper, we study genuine equivariant factorization homology and its interaction with equivariant Thom spectra, which we construct using the language of parametrized higher category theory. We describe the genuine equivariant factorization homology of Thom spectra, and use this description to compute several examples of interest. A key ingredient for our computations is an equivariant nonabelian Poincaré duality theorem, in which we prove that factorization homology with coefficients in a $G$-space is given by a mapping space. We compute the Real topological Hochschild homology ($THR$) of the Real bordism spectrum $M{U}_{\mathbb{R}}$ and of the equivariant Eilenberg--MacLane spectra $H{\underline{\mathbb{F}}}_2$ and $H{\underline{\mathbb{Z}}}_{(2)}$, as well as factorization homology of the sphere $S^{2\sigma }$ with coefficients in these Eilenberg--MacLane spectra. In Appendix B, Jeremy Hahn and Dylan Wilson compute $THR(H\underline{\mathbb{Z}})$.

Appendix by Jeremy Hahn and Dylan Wilson

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Cited by in corpus (3)

• On the geometric fixed-points of real topological cyclic homology
• A geometric approach to equivariant factorization homology and nonabelian Poincaré duality
• Parametrized higher category theory II: Universal constructions