分层伪流形的K-对偶
K-duality for stratified pseudomanifolds
摘要：
本文研究了一般分层伪流形K-理论中的Poincaré对偶。本文回顾了拓扑空间$X$的光滑分层$\fS$的公理化定义，并定义了一个广群$T^{\fS}X$，称为$\fS$ -切空间.这个广群是由编码层切空间的不同片段组成的，这些片段使用A.流形的切广群的Connes。主要结果是$C^{*}(T^{\fS}X)$是$C(X)$的Poincaré对偶，换句话说，$\fS$ -切空间在$X$的切空间的$K$ -理论中起作用.
英文摘要：
This paper is devoted to the study of Poincaré duality in K-theory for general stratified pseudomanifolds. We review the axiomatic definition of a smooth stratification $\fS$ of a topological space $X$ and we define a groupoid $T^{\fS}X$, called the $\fS$-tangent space. This groupoid is made of different pieces encoding the tangent spaces of the strata, and these pieces are glued into the smooth noncommutative groupoid $T^{\fS}X$ using the familiar procedure introduced by A. Connes for the tangent groupoid of a manifold. The main result is that $C^{*}(T^{\fS}X)$ is Poincaré dual to $C(X)$, in other words, the $\fS$-tangent space plays the role in $K$-theory of a tangent space for $X$.
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