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ON GEHRING–MARTIN–TAN GROUPS WITH AN ELLIPTIC GENERATOR

Part of: Low-dimensional topology Other groups of matrices

Published online by Cambridge University Press:  12 May 2016

DUŠAN REPOVŠ  and
ANDREI VESNIN
DUŠAN REPOVŠ*
Affiliation:
Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana, Kardeljeva pl. 16, 1000 Ljubljana, Slovenia email dusan.repovs@guest.arnes.si
ANDREI VESNIN
Affiliation:
Laboratory of Quantum Topology, Chelyabinsk State University, Chalyabinsk, Russia Sobolev Institute of Mathematics, Novosibirsk 630090, Russia email vesnin@math.nsc.ru
*
✉dusan.repovs@guest.arnes.si
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Abstract

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The Gehring–Martin–Tan inequality for two-generator subgroups of $\text{PSL}(2,\mathbb{C})$ is one of the best known discreteness conditions. A Kleinian group $G$ is called a Gehring–Martin–Tan group if the equality holds for the group $G$. We give a method for constructing Gehring–Martin–Tan groups with a generator of order four and present some examples. These groups arise as groups of finite-volume hyperbolic 3-orbifolds.

Keywords

hyperbolic orbifolddiscreteness conditiontwo-generated group

MSC classification

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 20H15: Other geometric groups, including crystallographic groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 2 , October 2016 , pp. 326 - 336
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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