关于奇异上同调的复盖的双复形的注解

Pub Date : 2021-01-01 DOI:10.4310/HHA.2021.V23.N2.A4

R. Frigerio, A. Maffei

{"title":"关于奇异上同调的复盖的双复形的注解","authors":"R. Frigerio, A. Maffei","doi":"10.4310/HHA.2021.V23.N2.A4","DOIUrl":null,"url":null,"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.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A remark on the double complex of a covering for singular cohomology\",\"authors\":\"R. Frigerio, A. Maffei\",\"doi\":\"10.4310/HHA.2021.V23.N2.A4\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/HHA.2021.V23.N2.A4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/HHA.2021.V23.N2.A4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 2

摘要

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。

查看原文

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

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助