Enumerating Kleinian Groups

David Gabai, Robert Meyerhoff, Nathaniel Thurston, Andrew Yarmola

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this manuscript, we give an overview of the tools and techniques needed for successfully classifying “low-complexity” Kleinian groups. In particular, we focus on extracting topological and geometric properties of discrete Kleinian groups, such as bounds on tube radii, cusp geometry, volume, relators in group presentation, and similar quantities. A key point of this manuscript is to explain how a discrete set of solutions (or their closure) can be found using continuous methods, in particular by searching over a continuous parameter space of groups. These methods provide an effective avenue for studying and classifying hyperbolic 3-manifolds that satisfy some geometric or topological constraints.

Original languageEnglish (US)
Title of host publicationComputational Aspects of Discrete Subgroups of Lie Groups
EditorsAlla Detinko, Michael Kapovich, Alex Kontorovich, Peter Sarnak, Richard Schwartz
PublisherAmerican Mathematical Society
Number of pages25
ISBN (Print)9781470468040
StatePublished - 2023
EventVirtual Conference on Computational Aspects of Discrete Subgroups of Lie Groups, 2021 - Virtual, Online
Duration: Jun 14 2021Jun 18 2021

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627


ConferenceVirtual Conference on Computational Aspects of Discrete Subgroups of Lie Groups, 2021
CityVirtual, Online

All Science Journal Classification (ASJC) codes

  • General Mathematics


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