Vol. 10, No. 1, 2009

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Buildings with isolated subspaces and relatively hyperbolic Coxeter groups

Pierre-Emmanuel Caprace

Vol. 10 (2009), No. 1, 15–31

Let (W,S) be a Coxeter system. We give necessary and sufficient conditions on the Coxeter diagram of (W,S) for W to be relatively hyperbolic with respect to a collection of finitely generated subgroups. The peripheral subgroups are necessarily parabolic subgroups (in the sense of Coxeter group theory). As an application, we present a criterion for the maximal flats of the Davis complex of (W,S) to be isolated. If this is the case, then the maximal affine sub-buildings of any building of type (W,S) are isolated.

Coxeter group, building, isolated flat, relative hyperbolicity
Mathematical Subject Classification 2000
Primary: 20E42, 20F55, 20F67, 20F69
Received: 26 September 2007
Accepted: 30 May 2009
Pierre-Emmanuel Caprace
Departement de Mathematiques
Universite Catholique de Louvain - IRMP
Chemin du Cyclotron 2, boîte L7.01.02
1348 Louvain-la-Neuve