On the asymmetry of stars at infinity
Group Theory
2020-01-20 v1 Geometric Topology
Abstract
Given a bordified space, Karlsson defines an incidence geometry of stars at infinity. These stars and their incidence are closely related to well-understood objects when the space is hyperbolic, CAT(0), or a bounded convex domain with the Hilbert metric. A question stemming from Karlsson's original paper was whether or not the relation of one boundary point being included in a star of another boundary point is symmetric. This paper provides an example demonstrating that this relation in the star boundary of the three-tree Diestel-Leader graph is not symmetric. In doing so, some interesting bounds on distance in Diestel-Leader graphs are utilized.
Keywords
Cite
@article{arxiv.2001.06411,
title = {On the asymmetry of stars at infinity},
author = {Keith Jones and Gregory A. Kelsey},
journal= {arXiv preprint arXiv:2001.06411},
year = {2020}
}
Comments
10 pages