#### Volume 9, issue 3 (2005)

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A better proof of the Goldman–Parker conjecture

### Richard Evan Schwartz

Geometry & Topology 9 (2005) 1539–1601
 arXiv: math.GR/0508202
##### Abstract

The Goldman–Parker Conjecture classifies the complex hyperbolic $ℂ$–reflection ideal triangle groups up to discreteness. We proved the Goldman–Parker Conjecture in an earlier paper 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
##### Mathematical Subject Classification 2000
Primary: 20F67
Secondary: 20F65, 20F55