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Notes on complex hyperbolic triangle groups
Author(s):
Shigeyasu
Kamiya;
John
R.
Parker;
James
M.
Thompson
Journal:
Conform. Geom. Dyn.
14
(2010),
202-218.
MSC (2010):
Primary 22E40;
Secondary 51M10, 53C35, 53C55
Posted:
August 30, 2010
MathSciNet review:
2718204
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Additional information
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
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:
10.1090/S1088-4173-2010-00215-8
PII:
S 1088-4173(2010)00215-8
Received by editor(s):
December 17, 2009
Posted:
August 30, 2010
Copyright of article:
Copyright
2010,
American Mathematical Society
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