Examples of \(\mathbb{Z}\)-acyclic and contractible vertex-homogeneous simplicial complexes
type: Item
instance of: scholarly article
title: Examples of \(\mathbb{Z}\)-acyclic and contractible vertex-homogeneous simplicial complexes
zbMATH Open document ID: 1011.52007
published in: Discrete \& Computational Geometry
publication date: 2002-05-21T00:00:00Z
review text: This paper constructs examples of \(\mathbb Z\)-acyclic vertex-homogeneous simplicial complexes. A primary motivation for this work is the Evasiveness Conjecture for simplicial complexes, which conjectures that the only non-evasive vertex-homogeneous simplicial complexes are simplices. (Non-evasiveness is a stronger property than acyclicity.) One such example, in dimension 11, was first found by Bob Oliver. The current paper finds 7 such examples, one of them in dimension 5, by constructions arising from the spherical dodecahedron space. These examples are the starting point for infinite families of such complexes.
reviewed by: Laura Anderson
Mathematics Subject Classification ID: 52B99
Mathematics Subject Classification ID: 57Q91
Mathematics Subject Classification ID: 51M20
zbMATH DE Number: 1743171
zbMATH Keywords: vertex-homogeneous simplicial complexes
zbMATH Keywords: evasiveness
MaRDI profile type: Publication
full work available at URL: s00454-001-0057-4
OpenAlex ID: W2052519713
DOI: 10.1007/S00454-001-0057-4
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description: scientific article; zbMATH DE number 1743171