Groups, Geometry, and Dynamics

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Volume 2, Issue 2, 2008, pp. 223–244
DOI: 10.4171/GGD/37

Published online: 2008-06-30

Separating quasi-convex subgroups in 7-systolic groups

Frédéric Haglund[1] and Jacek Świątkowski[2]

(1) Université Paris-Sud, Orsay, France
(2) Uniwersytet Wrocławski, Wroclaw, Poland

Let Γ be a group acting without inversions and simply transitively on the top-dimensional simplices of some simply-connected simplicial complex X with “simplicial negative curvature”. Then the quasi-convex subgroups of Γ are convex-cocompact. Furthermore, if the action of Γ on X satisfies some additional condition called “extra-tilability”, the quasi-convex subgroups of Γ are separable, i.e., every such subgroup is the intersection of finite index subgroups. The latter result applies to a large class of “simplicially negatively curved” groups recently constructed by Januszkiewicz and the second author.

Keywords: Separable subgroup, quasi-convex subgroup, word hyperbolic group, systolic group

Haglund Frédéric, Świątkowski Jacek: Separating quasi-convex subgroups in 7-systolic groups. Groups Geom. Dyn. 2 (2008), 223-244. doi: 10.4171/GGD/37