Boundaries of groups with isolated flats are path connected
Group Theory
2019-10-18 v2 Geometric Topology
Abstract
A seminal result in geometric group theory is that a 1-ended hyperbolic group has a locally connected visual boundary. As a consequence, a 1-ended hyperbolic group also has a path connected visual boundary. In this paper, we study when this phenomenon occurs for CAT(0) groups. We show if a 1-ended CAT(0) group with isolated flats acts geometrically on a CAT(0) space, then the visual boundary of the space is path connected. As a corollary, we prove all CAT(0) groups with isolated flats are semistable at infinity.
Cite
@article{arxiv.1909.12360,
title = {Boundaries of groups with isolated flats are path connected},
author = {Michael Ben-Zvi},
journal= {arXiv preprint arXiv:1909.12360},
year = {2019}
}
Comments
35 pages, 6 figures. Corrected some typos, reworked background sections