Cones over the boundaries of nonshellable but constructible 3-balls
type: Item
instance of: scholarly article
title: Cones over the boundaries of nonshellable but constructible 3-balls
zbMATH Open document ID: 1103.52011
author: Satoshi Kamei
published in: Osaka Journal of Mathematics
publication date: 2004-10-28T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ojm/1153493518
review text: At present, the only known way (via short knots; see \textit{M. Hachimori} and \textit{G. M. Ziegler} [Math. Z. 235, No. 1, 159--171 (2000; Zbl 0965.57022)]) to construct nonshellable simplicial \(3\)-spheres yields examples that are nonconstructible. Thus, it remains unclear whether there are nonshellable but constructible \(3\)-spheres. In this paper, the author investigates \(3\)-spheres that are obtained as the cones over nonshellable but constructible \(3\)-balls. It is shown that if a (constructible) simplicial \(3\)-ball can be decomposed into two shellable \(3\)-balls such that their intersection is a \(2\)-ball, then the cone over its boundary yields a shellable \(3\)-sphere. Shellability of the resulting \(3\)-spheres is also proved for the case of more complicated constructible \(3\)-balls.
Mathematics Subject Classification ID: 52B22
Mathematics Subject Classification ID: 57Q15
zbMATH DE Number: 2111462
zbMATH Keywords: shellability
zbMATH Keywords: constructibility
zbMATH Keywords: simplicial balls and spheres
MaRDI profile type: Publication
reviewed by: Frank H. Lutz
description: scientific article; zbMATH DE number 2111462