English

A homological nerve theorem for open covers

Algebraic Topology 2022-10-04 v1

Abstract

In this note we show that a particular homological nerve theorem, which was originally proved for a finite cover of a simplicial complex by subcomplexes, also holds for an open cover of an arbitrary topological space. The motivation for this is to affirmatively answer a question about the homology groups of Vietoris metric thickenings.

Keywords

Cite

@article{arxiv.2210.00388,
  title  = {A homological nerve theorem for open covers},
  author = {Patrick Gillespie},
  journal= {arXiv preprint arXiv:2210.00388},
  year   = {2022}
}

Comments

7 pages, 1 figure

R2 v1 2026-06-28T02:32:12.034Z