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arXiv · 2609.23528

Homological critical points for hypergraphs and simplicial complexes

Shiquan Ren
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Abstract

In this paper, we study the homological critical points for persistence hypergraphs and persistence simplicial complexes. With the help of the relative homology groups, we define the homological crtical points for persistence morphisms between persistence hypergraphs and persistence simplicial maps between persistence simplicial complexes. We prove some commutative diagrams of subset relations for the homological critical points of persistence hypergraphs as well as persistence morphisms between them. We also prove some commutative diagrams of subset relations for the homological critical points of persistence simplicial complexes as well as persistence simplicial maps between them. By using the parametric configuration spaces, we give the parametric independence complexes to be the space of packings and give the parametric dominating hypergraphs to be the space of coverings, as some examples.

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BibTeXRIS

Shiquan Ren. 2026-09-20. Homological critical points for hypergraphs and simplicial complexes. https://arxiv.org/abs/2609.23528

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