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2019 On the coarse geometry of certain right-angled Coxeter groups
Hoang Thanh Nguyen, Hung Cong Tran
Algebr. Geom. Topol. 19(6): 3075-3118 (2019). DOI: 10.2140/agt.2019.19.3075

Abstract

Let Γ be a connected, triangle-free, planar graph with at least five vertices that has no separating vertices or edges. If the graph Γ is CS, we prove that the right-angled Coxeter group GΓ is virtually a Seifert manifold group or virtually a graph manifold group and we give a complete quasi-isometry classification of these groups. Furthermore, we prove that GΓ is hyperbolic relative to a collection of CS right-angled Coxeter subgroups of GΓ. Consequently, the divergence of GΓ is linear, quadratic or exponential. We also generalize right-angled Coxeter groups which are virtually graph manifold groups to certain high-dimensional right-angled Coxeter groups (our families exist in every dimension) and study the coarse geometry of this collection. We prove that strongly quasiconvex, torsion-free, infinite-index subgroups in certain graph of groups are free and we apply this result to our right-angled Coxeter groups.

Citation

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Hoang Thanh Nguyen. Hung Cong Tran. "On the coarse geometry of certain right-angled Coxeter groups." Algebr. Geom. Topol. 19 (6) 3075 - 3118, 2019. https://doi.org/10.2140/agt.2019.19.3075

Information

Received: 17 August 2018; Revised: 31 December 2018; Accepted: 3 March 2019; Published: 2019
First available in Project Euclid: 29 October 2019

zbMATH: 07142626
MathSciNet: MR4023336
Digital Object Identifier: 10.2140/agt.2019.19.3075

Subjects:
Primary: 20F65, 20F67

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 6 • 2019
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