Tits boundary of CAT(0) 2-complexes
Group Theory
2007-05-23 v1 Geometric Topology
Abstract
We investigate the Tits boundary of locally compact CAT(0) 2-complexes. In particular we show that away from the endpoints, a geodesic segment in the Tits boundary is the ideal boundary of an isometrically embedded Euclidean sector. As applications, we provide sufficient conditions for two points in the Tits boundary to be the endpoints of a geodesic in the 2-complex and for a group generated by two hyperbolic isometries to contain a free group. We also show that if two CAT(0) 2-complexes are quasi-isometric then the cores of their Tits boundaries are bi-Lipschitz.
Cite
@article{arxiv.math/0303133,
title = {Tits boundary of CAT(0) 2-complexes},
author = {Xiangdong Xie},
journal= {arXiv preprint arXiv:math/0303133},
year = {2007}
}
Comments
26 pages