Nonplanar graphs in boundaries of CAT(0) groups
Geometric Topology
2018-07-09 v1 Group Theory
Abstract
Croke and Kleiner constructed two homeomorphic locally CAT(0) complexes whose universal covers have visual boundaries that are not homeomorphic. We construct two homeomorphic locally CAT(0) complexes so that the visual boundary of one universal cover contains a nonplanar graph, while the visual boundary of the other does not. In contrast, we prove for any two locally CAT(0) metrics on the Croke-Kleiner complex, if a finite graph embeds in the visual boundary of one universal cover, then the graph embeds in the visual boundary of the other.
Cite
@article{arxiv.1807.02439,
title = {Nonplanar graphs in boundaries of CAT(0) groups},
author = {Kevin Schreve and Emily Stark},
journal= {arXiv preprint arXiv:1807.02439},
year = {2018}
}
Comments
18 pages, 2 figures