Reflection trees of graphs as boundaries of Coxeter groups
Group Theory
2021-03-10 v1
Abstract
To any finite graph (viewed as a topological space) we assosiate some explicit compact metric space which we call {\it the reflection tree of graphs }. This space is of topological dimension and its connected components are locally connected. We show that if is appropriately triangulated (as a simplicial graph for which is the geometric realization) then the visual boundary of the right angled Coxeter system with the nerve isomorphic to is homeomorphic to . For each , this yields in particular many word hyperbolic groups with Gromov boundary homeomorphic to the space .
Keywords
Cite
@article{arxiv.1905.07602,
title = {Reflection trees of graphs as boundaries of Coxeter groups},
author = {Jacek Świątkowski},
journal= {arXiv preprint arXiv:1905.07602},
year = {2021}
}
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53 pages