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2021 Reflection trees of graphs as boundaries of Coxeter groups
Jacek Świątkowski
Algebr. Geom. Topol. 21(1): 351-420 (2021). DOI: 10.2140/agt.2021.21.351

Abstract

To any finite graph X (viewed as a topological space) we associate an explicit compact metric space 𝒳r(X), which we call the reflectiontree of graphs X. This space is of topological dimension 1 and its connected components are locally connected. We show that if X is appropriately triangulated (as a simplicial graph Γ for which X is the geometric realization) then the visual boundary (W,S) of the right-angled Coxeter system (W,S) with the nerve isomorphic to Γ is homeomorphic to 𝒳r(X). For each X, this yields in particular many word hyperbolic groups with Gromov boundary homeomorphic to the space 𝒳r(X).

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Jacek Świątkowski. "Reflection trees of graphs as boundaries of Coxeter groups." Algebr. Geom. Topol. 21 (1) 351 - 420, 2021. https://doi.org/10.2140/agt.2021.21.351

Information

Received: 27 August 2019; Accepted: 15 June 2020; Published: 2021
First available in Project Euclid: 16 March 2021

Digital Object Identifier: 10.2140/agt.2021.21.351

Subjects:
Primary: 20F65, 20F67
Secondary: 20F55, 57M07

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.21 • No. 1 • 2021
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