Spherical complexes

Fuente: arXiv
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Main Authors: Faridi, Sara, Holleben, Thiago
Format: Preprint
Published: 2023
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author Faridi, Sara
Holleben, Thiago
author_facet Faridi, Sara
Holleben, Thiago
contents In this paper we define spherical complexes as simplicial complexes with the property that every subcomplex obtained by a sequence of links and deletions either has trivial homology, or has the homology of a sphere. Examples of such complexes are independence complexes of ternary graphs and independence complexes of simplicial forests. We give criteria for when a spherical complex is acyclic, and describe the dimension of the sphere when it is not. We then apply our results to compute the Leray number of these complexes, and define combinatorial invariants for them which are counterparts to algebraic invariants of their Stanley-Reisner rings.
format Preprint
id arxiv_https___arxiv_org_abs_2311_07727
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Spherical complexes
Faridi, Sara
Holleben, Thiago
Commutative Algebra
Algebraic Topology
Combinatorics
13F55, 05E40, 05E45, 55U10, 55P15
In this paper we define spherical complexes as simplicial complexes with the property that every subcomplex obtained by a sequence of links and deletions either has trivial homology, or has the homology of a sphere. Examples of such complexes are independence complexes of ternary graphs and independence complexes of simplicial forests. We give criteria for when a spherical complex is acyclic, and describe the dimension of the sphere when it is not. We then apply our results to compute the Leray number of these complexes, and define combinatorial invariants for them which are counterparts to algebraic invariants of their Stanley-Reisner rings.
title Spherical complexes
topic Commutative Algebra
Algebraic Topology
Combinatorics
13F55, 05E40, 05E45, 55U10, 55P15
url https://arxiv.org/abs/2311.07727