A remark on the double complex of a covering for singular cohomology

IF 0.5 4区数学 Q2 MATHEMATICS Homology Homotopy and Applications Pub Date : 2021-01-01 DOI:10.4310/HHA.2021.V23.N2.A4

R. Frigerio, A. Maffei

引用次数: 2

Abstract

Given an open covering of a paracompact topological space X , there are two natural ways to construct a map from the cohomology of the nerve of the covering to the cohomology of X . One of them is based on a partition of unity, and is more topological in nature, while the other one relies on the double complex associated to an open covering, and has a more algebraic ﬂavour. In this paper we prove that these two maps coincide.

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关于奇异上同调的复盖的双复形的注解

给定一个准紧拓扑空间X的开覆盖，有两种自然的方法来构造从覆盖神经的上同调到X的上同调的映射。其中一个是基于统一的分割，并且在本质上更具有拓扑性，而另一个依赖于与开放覆盖相关的双重复合体，并且具有更多的代数味道。本文证明了这两个映射是重合的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

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审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.

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