Integral homology groups of double coverings and rank one ℤ-local systems for a minimal CW complex

Author:

Liu Ye,Liu Yongqiang

Abstract

Given a finite CW complex X X , a nonzero cohomology class ω H 1 ( X , Z 2 ) \omega \in H^1(X,\mathbb {Z}_2) determines a double covering X ω X^\omega and a rank one Z \mathbb {Z} -local system L ω \mathcal {L}_\omega . We investigate the relations between the homology groups H ( X ω , Z ) H_*(X^{\omega },\mathbb {Z}) and H ( X , L ω ) H_*(X,\mathcal {L}_\omega ) , when X X is homotopy equivalent to a minimal CW complex. In particular, this settles a conjecture recently proposed by Ishibashi, Sugawara and Yoshinaga [Betti numbers and torsions in homology groups of double coverings, arxiv.org/abs/2209.02236, 2022, Conjecture 3.3], for a hyperplane arrangement complement.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference10 articles.

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2. [ISY22] S. Ishibashi, S. Sugawara, and M. Yoshinaga, Betti numbers and torsions in homology groups of double coverings, arXiv:2209.02236, 2022.

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