A topological colorful Helly theorem
type: Item
instance of: scholarly article
title: A topological colorful Helly theorem
zbMATH Open document ID: 1064.52008
author: Gil Kalai
author: Roy Meshulam
published in: Advances in Mathematics
publication date: 2005-01-17T00:00:00Z
review text: Let \(X\) denote a simplicial complex. If \(H_j(X)\) is the \(j\)th homology group of \(X\) with rational coefficients, then the reduced rational homology is denoted by \(\widetilde H_j(Y)\). Let \(d\) be a positive integer. If \(\widetilde H_i(Y) = 0\) for all induced subcomplexes \(Y\) of \(X\) and all \(i \geq d\), then \(X\) is called \(d\)-Leray. The main result of this paper is the following extension of the colorful Helly theorem to \(d\)-Leray complexes: if \(X\) is a \(d\)-Leray complex on a vertex set \(V\) and \(M\subset X\) is a matroidal complex on \(V\) with rank function \(\rho\), then there exists a simplex \(\tau \in X\) such that \(\rho(V-\tau) \leq d\).
reviewed by: Marek Lassak
Mathematics Subject Classification ID: 52A35
Mathematics Subject Classification ID: 13F55
zbMATH DE Number: 2128862
zbMATH Keywords: Helly's theorem
zbMATH Keywords: simplicial topology
MaRDI profile type: Publication
full work available at URL: j.aim.2004.03.009
OpenAlex ID: W2053369489
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DOI: 10.1016/J.AIM.2004.03.009
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description: scientific article; zbMATH DE number 2128862