A non-shellable 3-sphere
type: Item
instance of: scholarly article
title: A non-shellable 3-sphere
zbMATH Open document ID: 0577.05031
DOI: 10.1016/S0195-6698(85)80026-3
author: Andrew Vince
published in: European Journal of Combinatorics
publication date: 1985-01-01T00:00:00Z
review text: Shellability of simplicial complexes has been a useful concept in polyhedral theory, in piecewise linear topology and more recently in connection with Cohen Macaulay rings. This paper initiates a study of shellability in a graph theoretic context. For certain graphs, called \(n\)-graphs, necessary and sufficient conditions for shellability are given. A correspondence is established between \(n\)-graphs and (\(n-1\))-dimensional simplicial complexes. Via this correspondence, results on shellability of \(n\)-graphs have implications for problems in PL-topology. For example, it is known that all 2-spheres and convex \(d\)-spheres are shellable. It has been conjectured that all 3-spheres are shellable. A counter-example is provided in the following sense. A finite cell complex is constructed whose cells are simplices and such that the underlying space is a 3-sphere whose simplices cannot be shelled.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 57M15
Mathematics Subject Classification ID: 57M40
zbMATH DE Number: 3922681
zbMATH Keywords: Shellability
zbMATH Keywords: simplicial complexes
zbMATH Keywords: n-graphs
zbMATH Keywords: 3-spheres
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3922681