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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Notes on complex hyperbolic triangle groups


Authors: Shigeyasu Kamiya, John R. Parker and James M. Thompson
Journal: Conform. Geom. Dyn. 14 (2010), 202-218
MSC (2010): Primary 22E40; Secondary 51M10, 53C35, 53C55
Published electronically: August 30, 2010
MathSciNet review: 2718204
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Abstract: We first demonstrate a family of isomorphisms between complex hyperbolic triangle groups and outline a systematic approach classifying the groups. Then we describe conditions that determine the discreteness of certain groups, in particular we prove a slightly weaker version of a conjecture given by Schwartz. Finally we collect together a list of known discrete triangle groups and propose some good candidates for discrete groups.


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Additional Information

Shigeyasu Kamiya
Affiliation: Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan
Email: s.kamiya@are.ous.ac.jp

John R. Parker
Affiliation: Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, United Kingdom
Email: j.r.parker@dur.ac.uk

James M. Thompson
Affiliation: Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, United Kingdom
Email: j.m.thompson@dur.ac.uk

DOI: http://dx.doi.org/10.1090/S1088-4173-2010-00215-8
PII: S 1088-4173(2010)00215-8
Received by editor(s): December 17, 2009
Published electronically: August 30, 2010
Article copyright: © Copyright 2010 American Mathematical Society