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Ideal triangle groups, dented tori, and numerical analysis

Richard Evan Schwartz
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Abstract

We prove the Goldman-Parker Conjecture: A complex hyperbolic ideal triangle group is directly 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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Richard Evan Schwartz. 2001-05-01. Ideal triangle groups, dented tori, and numerical analysis. https://arxiv.org/abs/math/0105264

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