Buildings with isolated subspaces and relatively hyperbolic Coxeter groups

2007/03/27 by Pierre-Emmanuel Caprace, Caprace, Pierre-Emmanuel · 2 citations
Mathematics · #20E42 #20F55 #20F67 #20F69 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20E42 #msc:20F55 #msc:20F67 #msc:20F69

paper · pdf · doi:10.48550/arxiv.math/0703799

An erratum, correcting two errors in the original paper, has been appended

arxiv created 2013/12/16 · arxiv updated 2013/12/17

Abstract

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.

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• Strong solidity classification of Coxeter groups
• Garside shadows and biautomatic structures in Coxeter groups

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