Homology, Homotopy and Applications
Volume 23 (2021)
A remark on the double complex of a covering for singular cohomology
Pages: 59 – 68
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.
nerve of a covering, double complex associated to an open covering
2010 Mathematics Subject Classification
55N05, 55N10, 55T99
Copyright © 2021, Roberto Frigerio and Andrea Maffei. Permission to copy for private use granted.
Received 7 March 2020
Received revised 2 July 2020
Accepted 11 October 2020
Published 7 April 2021