To any finite graph (viewed as a topological space) we associate an explicit compact metric space , which we call the reflectiontree 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 .
"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