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Ideal Triangle Groups, Dented Tori, and Numerical Analysis

Richard Evan Schwartz
Annals of Mathematics
Second Series, Vol. 153, No. 3 (May, 2001), pp. 533-598
Published by: Annals of Mathematics
DOI: 10.2307/2661362
Stable URL: http://www.jstor.org/stable/2661362
Page Count: 66
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Ideal Triangle Groups, Dented Tori, and Numerical Analysis
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Abstract

We prove the Goldman-Parker Conjecture: A complex hyperbolic ideal triangle group is discretely embedded in PU(2, 1) if and only if the product of its three standard generators is not elliptic. We also prove that such a group is indiscrete if the product of its three standard generators is elliptic. A novel feature of this paper is that it uses a rigorous computer assisted proof to deal with difficult geometric estimates.

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