Cohomology of open sets

2023/05/22 by Oliver Knill, Knill, Oliver
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2305.12613

Abstract

If G is a finite abstract simplicial complex and K is a subcomplex of G and U=G-K is the open complement of K in G, the Betti vectors of K and U and G satisfy the inequality b(G) less or equal b(K)+b(U).

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