A discreteness criterion for groups containing parabolic isometries
Geometric Topology
2023-09-06 v2 Dynamical Systems
Abstract
This note will prove a discreteness criterion for groups of orientation-preserving isometries of the hyperbolic space which contain a parabolic element. It can be viewed as a generalization of the well-known results of Shimizu-Leutbecher and Jorgensen in dimensions 2 and 3, and is closely related to Waterman's inequality in higher dimensions. Unlike his algebraic method, the argument presented here is geometric and yields an improved asymptotic bound.
Cite
@article{arxiv.1304.2298,
title = {A discreteness criterion for groups containing parabolic isometries},
author = {Viveka Erlandsson and Saeed Zakeri},
journal= {arXiv preprint arXiv:1304.2298},
year = {2023}
}
Comments
Substantially revised version, now covering all dimensions. 8 pages, 1 figure