Trees of manifolds as boundaries of spaces and groups
Group Theory
2020-09-30 v2 Geometric Topology
Abstract
We show that trees of manifolds, the topological spaces introduced by Jakobsche, appear as boundaries at infinity of various spaces and groups. In particular, they appear as Gromov boundaries of some hyperbolic groups, of arbitrary dimension, obtained by the procedure of strict hyperbolization. We also recognize these spaces as boundaries of arbitrary Coxeter groups with manifold nerves, and as Gromov boundaries of the fundamental groups of singular spaces obtained from some finite volume hyperbolic manifolds by cutting off their cusps and collapsing the resulting boundary tori to points.
Keywords
Cite
@article{arxiv.1304.5067,
title = {Trees of manifolds as boundaries of spaces and groups},
author = {Jacek Swiatkowski},
journal= {arXiv preprint arXiv:1304.5067},
year = {2020}
}
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23 pages