Notes on complex hyperbolic triangle groups
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- by Shigeyasu Kamiya, John R. Parker and James M. Thompson
- Conform. Geom. Dyn. 14 (2010), 202-218
- DOI: https://doi.org/10.1090/S1088-4173-2010-00215-8
- Published electronically: August 30, 2010
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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.References
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Bibliographic 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
- MR Author ID: 319072
- ORCID: 0000-0003-0513-3980
- 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
- Received by editor(s): December 17, 2009
- Published electronically: August 30, 2010
- © Copyright 2010 American Mathematical Society
- Journal: Conform. Geom. Dyn. 14 (2010), 202-218
- MSC (2010): Primary 22E40; Secondary 51M10, 53C35, 53C55
- DOI: https://doi.org/10.1090/S1088-4173-2010-00215-8
- MathSciNet review: 2718204