带角流形的余正规同调
Conormal homology of manifolds with corners
摘要：
给定一个有角点的流形$X$，我们将角点结构单纯复形$Σ_X$与它联系起来。它的约化K-同调同构于$X$上b-紧算子的$C^*$ -代数$\mathcal{K}_b(X)$的K-理论。此外，$Σ_X$的同调同构于$X$的余正规同调。对任意抽象有限单纯复形$Σ$，我们构造了一个角点为$X$的流形，使得$Σ_X\cong Σ$ .因此，有限单纯复形的同调和K-同调也作为带角流形的余法同调和它们的b-紧算子的K-理论而出现。特别地，这些群可以包含挠。
英文摘要：
Given a manifold with corners $X$, we associates to it the corner structure simplicial complex $Σ_X$. Its reduced K-homology is isomorphic to the K-theory of the $C^*$-algebra $\mathcal{K}_b(X)$ of b-compact operators on $X$. Moreover, the homology of $Σ_X$ is isomorphic to the conormal homology of $X$. In this note, we constract for an arbitrary abstract finite simplicial complex $Σ$ a manifold with corners $X$ such that $Σ_X\cong Σ$. As a consequence, the homology and K-homology which occur for finite simplicial complexes also occur as conormal homology of manifolds with corners and as K-theory of their b-compact operators. In particular, these groups can contain torsion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
