Geometry & Topology, Vol. 9 (2005) Paper no. 35, pages 1539--1601.

A better proof of the Goldman-Parker conjecture

Richard Evan Schwartz

Abstract. The Goldman-Parker Conjecture classifies the complex hyperbolic C-reflection ideal triangle groups up to discreteness. We proved the Goldman-Parker Conjecture in [Ann. of Math. 153 (2001) 533--598] using a rigorous computer-assisted proof. In this paper we give a new and improved proof of the Goldman-Parker Conjecture. While the proof relies on the computer for extensive guidance, the proof itself is traditional.

Keywords. Hyperbolic, complex reflection group, ideal triangle group, Goldman-Parker conjecture

AMS subject classification. Primary: 20F67. Secondary: 20F65, 20F55.

E-print: arXiv:math/0508202

DOI: 10.2140/gt.2005.9.1539

Submitted to GT on 8 February 2005. (Revised 2 July 2005.) Paper accepted 4 August 2005. Paper published 10 August 2005.

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Richard Evan Schwartz
Department of Mathematics, University of Maryland
Collage Park, MD 20742, USA
Email: res at math dot browm dot edu

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