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.File in questo prodotto:
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