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Cohomology of open sets

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arxiv 2305.12613 v1 pith:4GJHEGUC submitted 2023-05-22 cs.DM math.COmath.SP

Oliver Knill This is my paper · ORCID
classification cs.DMmath.COmath.SP
keywords openabstractbetticohomologycomplementcomplexequalfinite
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Remarks about Connection and Dirac matrices

    math.CO 2026-01 conditional novelty 5.0 of 10

    The eigenvalues of the connection and Dirac matrices of a finite simplicial complex are bounded above by the ordered connection and Dirac degrees, while the headline claim that the connection matrix dominates the Dira...

  2. Elements of finite geometry I

    math.HO 2026-08 unverdicted novelty 2.0 of 10

    A review-style snapshot of twelve finite-geometry theorems, each claiming a discrete analogue of a well-known continuum result.

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