论文标题
模棱两可分解同源性和非阿布尔庞加莱二元性的几何方法
A geometric approach to equivariant factorization homology and nonabelian Poincaré duality
论文作者
论文摘要
修复有限的G组G和N维正交G-代表V。我们使用两边的bar构造定义了$ E_V $ -Algebra中的V框架平滑G-Manifold的等效分解同源性，并在$ E_V $ -Algebra中使用系数[and10，km18]。该构建使用最少的分类背景，并实现最大的具体性，从而允许方便的关键特性证明，包括在切向结构变化下的均衡分解同源性的不变性。使用几何扫描地图，我们证明了由于几位作者而证明了非阿布莱庞贝里二元定理的e夫式版本（ENPD）。 ENPD指出，扫描图从等效分解同源性到映射空间时，当系数是G-manifolds时，绘制了G-manifolds的单点压实。对于非G连接系数，当G-manifolds中有合适的R副本时，扫描图可以完成组完成。这概括了[GM17]中V-折返空间的识别原理。
Fix a finite group G and an n-dimensional orthogonal G-representation V. We define the equivariant factorization homology of a V-framed smooth G-manifold with coefficients in an $E_V$-algebra using a two-sided bar construction, generalizing [And10, KM18]. This construction uses minimal categorical background and aims for maximal concreteness, allowing convenient proofs of key properties, including invariance of equivariant factorization homology under change of tangential structures. Using a geometrically-seen scanning map, we prove an equivariant version (eNPD) of the nonabelian Poincare duality theorem due to several authors. The eNPD states that the scanning map gives a G-equivalence from the equivariant factorization homology to mapping spaces out the one-point compactification of the G-manifolds when the coefficients are G-connected. For non-G-connected coefficients, when the G-manifolds have suitable copies of R in them, the scanning map gives group completions. This generalizes the recognition principle for V -fold loops spaces in [GM17].
