Polygonal complexes and combinatorial group theory
type: Item
instance of: scholarly article
title: Polygonal complexes and combinatorial group theory
zbMATH Open document ID: 0832.57002
DOI: 10.1007/BF01265309
published in: Geometriae Dedicata
publication date: 1996-03-07T00:00:00Z
review text: This paper aims at 2-dimensional complexes of nonpositive curvature. Classical examples are the regular tessellations \(\{p, q\}\), \({1\over p}+ {1\over q}\leq {1\over 2}\). In Chapters 1 and 2 the authors construct many \(k\)-complexes (consisting of \(k\)-gons) such that the link of each vertex is the 1-skeleton of an \(n\)-simplex or of an \(n\)-cube. In particular, regular complexes of this type and their groups are studied. Classification results are obtained, for \(k\geq 6\) and \(n\geq 4\) there is a uniqueness result. Chapter 3 of the paper gives an interesting relationship with the word problem and regular formal languages.
Mathematics Subject Classification ID: 57M20
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 57M60
zbMATH DE Number: 627548
zbMATH Keywords: hyperbolic groups
zbMATH Keywords: 2-dimensional complexes of nonpositive curvature
zbMATH Keywords: regular complexes
zbMATH Keywords: word problem
zbMATH Keywords: regular formal languages
author: Werner Ballmann
author: Michael Brin
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
Wikidata QID: Q56213067
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description: scientific article; zbMATH DE number 627548