Volume 14, issue 3 (2014)

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Algebraic ranks of $\mathrm{CAT}(0)$ groups

Raeyong Kim

Algebraic & Geometric Topology 14 (2014) 1627–1648
Abstract

We study the algebraic rank of various classes of CAT(0) groups. They include right-angled Coxeter groups, right-angled Artin groups, relatively hyperbolic groups and groups acting geometrically on CAT(0) spaces with isolated flats. As one of our corollaries, we obtain a new proof of a result on commensurability of Coxeter groups.

Keywords
algebraic rank of a group, $\mathrm{CAT}(0)$ groups, right-angled Coxeter groups, relatively hyperbolic groups
Mathematical Subject Classification 2010
Primary: 57M07
Secondary: 20F55, 20F65
References
Publication
Received: 4 October 2012
Revised: 2 July 2013
Accepted: 30 July 2013
Published: 29 May 2014
Authors
Raeyong Kim
Department of Mathematics
The Ohio State University
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