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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Notes on complex hyperbolic triangle groups
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by Shigeyasu Kamiya, John R. Parker and James M. Thompson PDF
Conform. Geom. Dyn. 14 (2010), 202-218 Request permission

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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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
  • 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