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Cohomology of open sets

Published 22 May 2023 in cs.DM, math.CO, and math.SP | (2305.12613v1)

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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