Gromov hyperbolic groups and the Macaev norm.
type: Item
instance of: scholarly article
title: Gromov hyperbolic groups and the Macaev norm.
zbMATH Open document ID: 1125.37007
author: Rui Okayasu
published in: Pacific Journal of Mathematics
publication date: 2007-02-26T00:00:00Z
review text: Let \(\Gamma\) be a Gromov hyperbolic group with a finite set \(A\) of generators. One can consider three quantities: the Coornaert-Papadopoulos topological entropy \(h_{top}(\Sigma(\infty))\) of the subshift associated to \((\Gamma,A)\), Voiculescu's invariant \(k^-_\infty(\lambda_A)\), and the growth entropy \(\text{gr}(\Gamma,A)\). The author proves that \(h_{top}(\Sigma(\infty))\leq k^-_\infty(\lambda_A)\leq\text{gr}(\Gamma,A)\) and that these invariants are equal for a hyperbolic group splitting over a finite group.
reviewed by: Klaudiusz Wójcik
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F67
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47A30
zbMATH DE Number: 5129574
zbMATH Keywords: hyperbolic groups
zbMATH Keywords: perturbation theory
zbMATH Keywords: Macaev ideal
MaRDI profile type: Publication
full work available at URL: pjm.2006.223.141
OpenAlex ID: W1995471804
DOI: 10.2140/PJM.2006.223.141
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description: scientific article; zbMATH DE number 5129574