Quasi-isometric rigidity for PSL(2,Z[1/p])
Group Theory
2007-05-23 v1 Geometric Topology
Abstract
We prove that PSL(2,Z[1/p]) gives the first example of groups which are not quasi-isometric to each other but have the same quasi-isometry group. Namely, PSL(2,Z[1/p]) and PSL(2,Z[1/q]) are not quasi-isometric unless p=q, and, independent of p, the quasi-isometry group of PSL(2,Z[1/p]) is PSL(2,Q). In addition, we characterize PSL(2,Z[1/p]) uniquely among all finitely generated groups by its quasi-isometry type.
Keywords
Cite
@article{arxiv.math/9809108,
title = {Quasi-isometric rigidity for PSL(2,Z[1/p])},
author = {Jennifer Taback},
journal= {arXiv preprint arXiv:math/9809108},
year = {2007}
}
Comments
29 pages, 4 figures, LaTeX, epsfig