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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2024 MCQ for Conformal Geometry and Dynamics is 0.49.

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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

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