Abstract

The canonical mapping of cohomology with compact supports via linear functionals on homology, generally speaking, is not surjective. The image of the mapping is described by linear functionals with compact supports. In this paper we prove the formula \(H_{c}^{k}(X;\mathbb{R})={\textrm{Hom}}_{c}(H_{k}^{c}(X;\mathbb{R}),\mathbb{R})\), where \(X\) is a countable simplicial complex with an additional requirement, the star of each simplex has a finite number of simplices in all dimensions.

中文翻译：

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关于紧支座上同调的对偶性

摘要

一般而言，通过线性泛函对上同调与紧支座的规范映射不是满射的。映射的图像由具有紧凑支持的线性泛函描述。在本文中，我们证明了公式\(H_{c}^{k}(X;\mathbb{R})={\textrm{Hom}}_{c}(H_{k}^{c}(X; \mathbb{R}),\mathbb{R})\)，其中\(X\)是一个具有附加要求的可数单纯复形，每个单纯形的星在所有维度上都有有限数量的单纯形。