Permuted difference cycles and triangulated sphere bundles
type: Item
instance of: scholarly article
title: Permuted difference cycles and triangulated sphere bundles
zbMATH Open document ID: 0866.52011
DOI: 10.1016/0012-365X(95)00287-7
author: Gunter Lassmann
author: Wolfgang Kühnel
published in: Discrete Mathematics
publication date: 1995-11-15T00:00:00Z
review text: As a generalization of the classical 7-vertex torus, a 2-parameter family of 2-neighborly triangulated \(d\)-manifolds \(M^d_k\) is constructed, each invariant under the action of the dihedral group \(D_n\) on \(n = 2^{d - k} (k + 3) - 1\) vertices. \(M^d_k\) occurs as the boundary of a \((d + 1)\)-manifold with the same properties. In particular, \(M^d_d\) is the boundary of a \((d + 1)\)-simplex, \(M^d_{d - 1}\) is the boundary of an orientable or nonorientable 1-handle depending on the parity of \(d\), \(M^d_1\) is a \(d\)-dimensional torus. Topologically \(M^d_k\) is the total space of a sphere bundle over a \((d - k)\)-dimensional torus. The construction of the triangulation itself is purely combinatorial. It is based on permutations of certain difference cycles encoding all the information about the triangulation in \(d\) integers.
Mathematics Subject Classification ID: 52B70
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 57Q15
zbMATH DE Number: 812489
zbMATH Keywords: cyclic group action
zbMATH Keywords: sphere bundles
zbMATH Keywords: disc bundles
zbMATH Keywords: neighborly triangulation
zbMATH Keywords: difference cycles
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 812489