稳定化后的非交换Poincare对偶
Nonabelian Poincare duality after stabilizing
摘要：
本文将Salvatore在[Sal 01]和Lurie在[Lur 09]中的非交换Poincare对偶定理推广到不一定群状的E_n-代数的情形（空间范畴）.我们定义了一个稳定化过程的基础上McDuff的“brining点从无穷大”的地图[McD 75]。对于开连通可平行n-流形，证明了在稳定化后，E_n-代数A中系数的M的拓扑手征同调与A的n重分类空间的紧支撑映射空间Map^c（M，B^n A）的同调等价.本文所用的两个拓扑手性同源模型是Andrade的[And10]模型和Salvatore的[Sal 01]模型。
英文摘要：
We generalize the nonabelian Poincare duality theorems of Salvatore in [Sal01] and Lurie in [Lur09] to the case of not necessarily grouplike E_n-algebras (in the category of spaces). We define a stabilization procedure based on McDuff's "brining points in from infinity" maps from [McD75]. For open connected parallelizable n-manifolds, we prove that, after stabilizing, the topological chiral homology of M with coefficients in an E_n-algebra A, is homology equivalent to Map^c(M,B^n A), the space of compactly supported maps to the n-fold classifying space of A. The two models of topological chiral homology used in this paper are Andrade's model from [And10] and Salvatore's from [Sal01].
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