Geodesic
A remark on the double complex of a covering for singular cohomology
Homology, homotopy, and applications, Tome 23 (2021) no. 2, pp. 59-68.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2021.v23.n2.a4
Classification : 55N05, 55N10, 55T99
Keywords: nerve of a covering, double complex associated to an open covering 
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Roberto Frigerio; Andrea Maffei. A remark on the double complex of a covering for singular cohomology. Homology, homotopy, and applications, Tome 23 (2021) no. 2, pp. 59-68. doi : 10.4310/HHA.2021.v23.n2.a4. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n2.a4/

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