A discreteness criterion for groups containing parabolic isometrics

Viveca Erlandsson, Saeed Zakeri

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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.

Original languageEnglish
Title of host publicationGEOMETRY, GROUPS AND DYNAMICS
EditorsCS Aravinda, WM Goldman, K Gongopadhyay, A Lubotzky, M Mj, A Weaver
PublisherAMERICAN MATHEMATICAL SOCIETY
Pages235-242
Number of pages8
ISBN (Print)978-0-8218-9882-6
DOIs
Publication statusPublished - 2015
MoE publication typeA4 Article in a conference publication
EventConference on the ICTS Program: Groups, Geometry and Dynamics - Almora, India
Duration: 3 Dec 201216 Dec 2012

Publication series

NameContemporary Mathematics
PublisherAMER MATHEMATICAL SOC
Volume639
ISSN (Print)0271-4132

Conference

ConferenceConference on the ICTS Program
Abbreviated titleGGD
CountryIndia
CityAlmora
Period03/12/201216/12/2012

Keywords

  • Screw parabolic elements
  • Margulis region
  • Shimizu's lemma
  • Jorgensen's inequality
  • MOBIUS TRANSFORMATIONS

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