论文标题
thom光谱的doivariant nonabelianpoincaré二元性和等效分解同源性
Equivariant nonabelian Poincaré duality and equivariant factorization homology of Thom spectra
论文作者
论文摘要
在本文中，我们研究了真正的模棱两可的分解同源性及其与thom光谱的相互作用，我们使用参数化的高等类别理论的语言构建了它们。我们描述了THOM光谱的真实性分解同源性，并使用此描述来计算几个感兴趣的例子。我们计算的关键要素是一个模棱两可的北极元素二元定理，在其中，我们证明，映射空间给出了与系数的分解同源性。我们计算真实的无孔谱的真实拓扑同源（$ thr $）$ mu_ \ mathbb {r} $和Equivariant eilenberg--maclane spectra $ h \ h \ spectra $ h \ spectra $ h \ useverline {\ mathbb {f}以及在这些eilenberg--maclane光谱中具有系数的球体的分解同源性$ s^{2σ} $。在附录B中，杰里米·哈恩（Jeremy Hahn）和迪伦·威尔逊（Dylan Wilson）计算$ thr（h \ underline {\ mathbb {z}}}）$。
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 $THR(H\underline{\mathbb{Z}})$.
