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Computing arithmetic Kleinian groups


Author: Aurel Page
Journal: Math. Comp. 84 (2015), 2361-2390
MSC (2010): Primary 11F06, 11Y99, 30F40; Secondary 11-04, 16U60, 11R52
DOI: https://doi.org/10.1090/S0025-5718-2015-02939-1
Published electronically: March 13, 2015
MathSciNet review: 3356030
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Abstract: Arithmetic Kleinian groups are arithmetic lattices in  $ \mathrm {PSL}_2(\mathbb{C})$. We present an algorithm that, given such a group $ \Gamma $, returns a fundamental domain and a finite presentation for $ \Gamma $ with a computable isomorphism.


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Additional Information

Aurel Page
Affiliation: Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France, CNRS, IMB, UMR 5251, F-33400 Talence, France, INRIA, F-33400 Talence, France
Email: aurel.page@math.u-bordeaux1.fr; a.r.page@warwick.ac.uk

DOI: https://doi.org/10.1090/S0025-5718-2015-02939-1
Received by editor(s): May 31, 2012
Received by editor(s) in revised form: February 6, 2013, September 20, 2013, and February 2, 2014
Published electronically: March 13, 2015
Article copyright: © Copyright 2015 American Mathematical Society