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
Kim, Raeyong 1
@article{10_2140_agt_2014_14_1627,
author = {Kim, Raeyong},
title = {Algebraic ranks of {CAT(0)} groups},
journal = {Algebraic and Geometric Topology},
pages = {1627--1648},
year = {2014},
volume = {14},
number = {3},
doi = {10.2140/agt.2014.14.1627},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2014.14.1627/}
}
Kim, Raeyong. Algebraic ranks of CAT(0) groups. Algebraic and Geometric Topology, Tome 14 (2014) no. 3, pp. 1627-1648. doi: 10.2140/agt.2014.14.1627
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