On modular homology of simplicial complexes: Saturation
type: Item
instance of: scholarly article
title: On modular homology of simplicial complexes: Saturation
zbMATH Open document ID: 1012.52020
author: Valeriy B. Mnukhin
author: I. J. Siemons
published in: Journal of Combinatorial Theory. Series A
publication date: 2003-06-10T00:00:00Z
full work available at URL: On modular homology of simplicial complexes-saturation-2002.pdf
review text: This article is a continuation of [J. Comb. Theory, Ser. A 93, 350-370 (2001; Zbl 0971.06006)] where the authors considered a homology-like theory called modular homology applied to shellable simplicial complexes. There it was shown that the modular homology of a shellable complex is not determined by its \(h\)-vector. The article under review should be read together with that article. In the article under review, it is shown that the homology of a shellable complex can nonetheless be embedded in a module constructed purely from the shelling of the complex. From this, the authors are able to prove certain simple bounds on the Betti numbers of the complex. Complexes attaining these bounds are called saturated complexes. The authors also study conditions under which a shellable complex is saturated, and are able to give sufficient conditions under which gluing a simplex to a saturated complex yields still another saturated complex. Towards the end, the results are applied to Coxeter complexes and buildings.
Mathematics Subject Classification ID: 52B22
Mathematics Subject Classification ID: 06A11
Mathematics Subject Classification ID: 05E25
zbMATH DE Number: 1760687
zbMATH Keywords: modular homology
zbMATH Keywords: inclusion map
zbMATH Keywords: simplicial complex
zbMATH Keywords: Betti numbers
zbMATH Keywords: shellability
zbMATH Keywords: Coxeter complex
zbMATH Keywords: building
zbMATH Keywords: saturation
reviewed by: Michael I. Hartley
describes a project that uses: Simplicial complex library
MaRDI profile type: Publication
OpenAlex ID: W2473168016
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DOI: 10.1006/JCTA.2001.3247
description: scientific article; zbMATH DE number 1760687