2019/12/16 by Roberto Frigerio, Frigerio, Roberto, Andrea Maffei +1
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1912.07736
openalex publication_date 2019/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an open cover of a paracompact topological space X, there are two natural ways to construct a map from the cohomology of the nerve of the cover 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 Mayer-Vietoris double complex, and has a more algebraic flavour. In this paper we prove that these two maps coincide, thus answering a question posed by N. V. Ivanov.