Boundaries of Hyperbolic Metric Spaces
Metric Geometry
2007-05-23 v1 Group Theory
Operator Algebras
Abstract
We investigate the relationship between the metric boundary and the Gromov boundary of a hyperbolic metric space. We show that the Gromov boundary is a quotient topological space of the metric boundary, and that therefore a word-hyperbolic group has an amenable action on the metric boundary of its Cayley graph. This result has significance for the study of Lip-norms on group C*-algebras.
Cite
@article{arxiv.math/0310101,
title = {Boundaries of Hyperbolic Metric Spaces},
author = {Corran Webster and Adam Winchester},
journal= {arXiv preprint arXiv:math/0310101},
year = {2007}
}
Comments
9 pages. AMSLaTeX