等变非阿贝尔庞加莱对偶性与Thom谱的等变因子同调
Equivariant nonabelian Poincaré duality and equivariant factorization homology of Thom spectra
AI总结：
该研究利用参数化高范畴论构造等变Thom谱，证明等变非阿贝尔庞加莱对偶定理，刻画Thom谱的等变因子同调并完成多类谱与球面的相关同调计算。
摘要：
本文研究真正的等变因子同调及其与等变Thom谱的相互作用，我们使用参数化高范畴论的语言构造了等变Thom谱。我们刻画了Thom谱的真正等变因子同调，并利用该刻画计算了若干有价值的例子。我们计算的一个关键要素是等变非阿贝尔庞加莱对偶定理，在该定理中我们证明了以G-空间为系数的因子同调由一个映射空间给出。我们计算了实配边谱$MU_\mathbb{R}$、等变Eilenberg–MacLane谱$H\underline{\mathbb{F}}_2$与$H\underline{\mathbb{Z}}_{(2)}$的实拓扑霍赫希尔德同调（$THR$），还计算了球面$S^{2σ}$以这些Eilenberg–MacLane谱为系数的因子同调。在附录B中，Jeremy Hahn和Dylan Wilson计算了$THR(H\underline{\mathbb{Z}})$。
英文摘要：
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 $MU_\mathbb{R}$ 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 $S^{2σ}$ with coefficients in these Eilenberg--MacLane spectra. In Appendix B, Jeremy Hahn and Dylan Wilson compute $THR(H\underline{\mathbb{Z}})$.
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