15-vertex triangulations of an 8-manifold
type: Item
instance of: scholarly article
title: 15-vertex triangulations of an 8-manifold
zbMATH Open document ID: 0734.57017
DOI: 10.1007/BF01934320
author: Ulrich Brehm
author: Wolfgang Kühnel
published in: Mathematische Annalen
publication date: 1992-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164996
review text: A combinatorial 8-manifold which is not PL homeomorphic to the sphere must have at least 15 vertices. Such an 8-manifold with 15 vertices must be a ``manifold like the quaternionic projective plane'' in the sense of J. Eells and N. H. Kuiper. In this paper we construct three such triangulations, the most symmetric one being invariant under a vertex transitive action of \(A_ 5\). Each of the three triangulations is 5- neighborly, i.e. it contains all \(15\choose 5\) 4-dimensional simplices. This induces a tight polyhedral embedding into \(E^{14}\) as a subcomplex of the 14-dimensional simplex. The three triangulations are PL homeomorphic to each other, we conjecture they are triangulations of the quaternionic projective plane.
Mathematics Subject Classification ID: 57Q99
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 4214962
zbMATH Keywords: combinatorial 8-manifold
zbMATH Keywords: polyhedral embedding
zbMATH Keywords: quaternionic projective plane
Wikidata QID: Q105623807
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4214962