Asymptotic behavior of word metrics on Coxeter groups.
type: Item
instance of: scholarly article
title: Asymptotic behavior of word metrics on Coxeter groups.
zbMATH Open document ID: 1241.20046
published in: Documenta Mathematica
publication date: 2011-09-09T00:00:00Z
full work available at URL: 11.html
review text: Summary: We study the geometry of tessellation defined by the walls in the Moussong complex \(\mathcal M_W\) of a Coxeter group \(W\). It is proved that geodesics in \(\mathcal M_W\) can be approximated by geodesic galleries of the tessellation. A formula for the translation length of an element of \(W\) is given. We prove that the restriction of the word metric on the \(W\) to any free Abelian subgroup \(A\) is Hausdorff equivalent to a regular norm on \(A\).
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 51F15
zbMATH DE Number: 5947057
zbMATH Keywords: Coxeter groups
zbMATH Keywords: Moussong complexes
zbMATH Keywords: translation lengths
zbMATH Keywords: geodesic galleries
zbMATH Keywords: tessellations
zbMATH Keywords: word metric
zbMATH Keywords: free Abelian subgroups
author: Gennady A. Noskov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5947057