Buildings with isolated subspaces and relatively hyperbolic Coxeter groups
By P. Caprace. 2007
54 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/16eb8b894fc8f6b81e6a0a5a8f9b594e5b364462
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In Discrete Mathematics and Combinatorics
- Daan Krammer
- P. Caprace
- K. Fujiwara
- Stephen Bigelow
- Juan González-Meneses
- Luis Paris
- Lenhard L. Ng
- Dan Boneh
In Geometry and Topology
- K. Fujiwara
- Daan Krammer
- P. Caprace
- Denis V. Osin
- Stephen Bigelow
- Luis Paris
- Juan González-Meneses
- Alessandro Sisto
Citations in the corpus
- Rank-One Isometries of Buildings and Quasi-Morphisms of Kac–Moody Groups (2008, background): “The same arguments as before then yield the desired conclusion. Proof of Proposition 1.7 . By [ Ca1 , Cor.”
- Hyperbolicities in CAT(0) cube complexes (2017, unknown): “h that the image of every combinatorial isometric embedding R2 → X is included into the C2-neighborhood of a translate of Yi for some 1 ≤ i ≤ n. In other contexts, similar statements can be found in [Cap09] and [HK09]. We begin by recalling [Gen17a, Lemma 8.6], which will be useful in the proof of o”
- The conjugacy problem for Coxeter groups (2009, methodology): “10 was subsequently used in [13], [18], [15].”