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.
Classification :
20-XX, 00-XX
Mots-clés :
Separable subgroup, quasi-convex subgroup, word hyperbolic group, systolic group
Affiliations des auteurs :
Frédéric Haglund
1
;
Jacek Świątkowski
2
1
Université Paris-Sud, Orsay, France
2
Uniwersytet Wrocławski, Wroclaw, Poland
Frédéric Haglund; Jacek Świątkowski. Separating quasi-convex subgroups in 7-systolic groups. Groups, geometry, and dynamics, Tome 2 (2008) no. 2, pp. 223-244. doi: 10.4171/ggd/37
@article{10_4171_ggd_37,
author = {Fr\'ed\'eric Haglund and Jacek \'Swi\k{a}tkowski},
title = {Separating quasi-convex subgroups in 7-systolic groups},
journal = {Groups, geometry, and dynamics},
pages = {223--244},
year = {2008},
volume = {2},
number = {2},
doi = {10.4171/ggd/37},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/37/}
}
TY - JOUR
AU - Frédéric Haglund
AU - Jacek Świątkowski
TI - Separating quasi-convex subgroups in 7-systolic groups
JO - Groups, geometry, and dynamics
PY - 2008
SP - 223
EP - 244
VL - 2
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/37/
DO - 10.4171/ggd/37
ID - 10_4171_ggd_37
ER -
%0 Journal Article
%A Frédéric Haglund
%A Jacek Świątkowski
%T Separating quasi-convex subgroups in 7-systolic groups
%J Groups, geometry, and dynamics
%D 2008
%P 223-244
%V 2
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/37/
%R 10.4171/ggd/37
%F 10_4171_ggd_37
