A discreteness criterion for groups containing parabolic isometries

Viveka Erlandsson; Saeed Zakeri

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arXiv · 1304.2298

A discreteness criterion for groups containing parabolic isometries

Viveka Erlandsson·Saeed Zakeri

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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.

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Viveka Erlandsson, Saeed Zakeri. 2013-04-08. A discreteness criterion for groups containing parabolic isometries. https://arxiv.org/abs/1304.2298

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