Nonhyperbolic Coxeter groups with Menger curve boundary (with erratum)
Group Theory
2020-05-18 v5 Geometric Topology
Abstract
A generic finite presentation defines a word hyperbolic group whose boundary is homeomorphic to the Menger curve. In this article, we produce the first known examples of non-hyperbolic groups whose visual boundary is homeomorphic to the Menger curve. The examples in question are the Coxeter groups whose nerve is a complete graph on vertices for . The construction depends on a slight extension of Sierpi\'nski's theorem on embedding --dimensional planar compacta into the Sierpi\'nski carpet. See the appendix for a brief erratum.
Cite
@article{arxiv.1812.04649,
title = {Nonhyperbolic Coxeter groups with Menger curve boundary (with erratum)},
author = {Matthew Haulmark and G. Christopher Hruska and Bakul Sathaye},
journal= {arXiv preprint arXiv:1812.04649},
year = {2020}
}
Comments
15 pages, 2 figures. This updated version contains a brief erratum correcting an error in the previous versions