Algebraic ranks of CAT(0) groups

Kim, Raeyong

doi:10.2140/agt.2014.14.1627

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

Raeyong Kim

Algebraic & Geometric Topology 14 (2014) 1627–1648

DOI: 10.2140/agt.2014.14.1627

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 231 West 18th Avenue Columbus, OH 43210-1174 USA

Volume 14, issue 3 (2014)