Innovations in Incidence Geometry

Buildings with isolated subspaces and relatively hyperbolic Coxeter groups

Pierre-Emmanuel Caprace

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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.

Article information

Source
Innov. Incidence Geom., Volume 10, Number 1 (2009), 15-31.

Dates
Received: 26 September 2007
Accepted: 30 May 2009
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323102

Digital Object Identifier
doi:10.2140/iig.2009.10.15

Mathematical Reviews number (MathSciNet)
MR2665193

Zentralblatt MATH identifier
1254.20036

Subjects
Primary: 20E42: Groups with a $BN$-pair; buildings [See also 51E24] 20F55: Reflection and Coxeter groups [See also 22E40, 51F15] 20F67: Hyperbolic groups and nonpositively curved groups 20F69: Asymptotic properties of groups

Keywords
Coxeter group building isolated flat relative hyperbolicity

Citation

Caprace, Pierre-Emmanuel. Buildings with isolated subspaces and relatively hyperbolic Coxeter groups. Innov. Incidence Geom. 10 (2009), no. 1, 15--31. doi:10.2140/iig.2009.10.15. https://projecteuclid.org/euclid.iig/1551323102


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References

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