Ideal Triangle Groups, Dented Tori, and Numerical Analysis

Richard Evan Schwartz
2001 Annals of Mathematics  
We prove the Goldman-Parker Conjecture: A complex hyperbolic ideal triangle group is discretely embedded in P U (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.
doi:10.2307/2661362 fatcat:goqmlk5mgnbqlfmvrlqx7weauq