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.

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

Roberto Frigerio
;
Andrea Maffei
2021-01-01

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.
2021
Frigerio, Roberto; Maffei, Andrea
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1048758
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