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On the set of discrete two-generator groups

Published online by Cambridge University Press:  01 March 2000

LINE BARIBEAU  and
THOMAS RANSFORD
LINE BARIBEAU
Affiliation:
Département de mathématiques et de statistique, Université Laval, Québec (Québec), Canada G1K 7P4
THOMAS RANSFORD
Affiliation:
Département de mathématiques et de statistique, Université Laval, Québec (Québec), Canada G1K 7P4
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Abstract

A two-generator group 〈f, g〉 of Möbius maps is determined, up to conjugacy, by the numbers β = tr2(f) − 4, β′ = tr2(g) − 4 and γ = tr (fgf−1g−1) − 2, provided that γ ≠ 0. We study the subset D of C3 of those (β, β′, γ) which arise from discrete groups. In particular, we identify precisely D[setmn ]D.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 128 , Issue 2 , March 2000 , pp. 245 - 255
Copyright
© The Cambridge Philosophical Society 2000

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Footnotes

Research supported by grants from the Natural Sciences and Engineering Research Council of Canada and the Fonds FCAR of Québec.