Right-angled Artin group boundaries
Group Theory
2019-10-18 v1 Geometric Topology
Abstract
In all known examples of a CAT(0) group acting on CAT(0) spaces with non-homeomorphic CAT(0) visual boundaries, the boundaries are each not path connected. In this paper, we show this does not have to be the case by providing examples of right-angled Artin groups which exhibit non-unique CAT(0) boundaries where all of the boundaries are arbitrarily connected. We also prove a combination theorem for certain amalgams of CAT(0) groups to act on spaces with non-path connected visual boundaries. We apply this theorem to some right-angled Artin groups.
Keywords
Cite
@article{arxiv.1910.07560,
title = {Right-angled Artin group boundaries},
author = {Michael Ben-Zvi and Robert Kropholler},
journal= {arXiv preprint arXiv:1910.07560},
year = {2019}
}
Comments
13 pages, 3 figures