Geometry & Topology 9 (2005) 1539–1601

DOI: 10.2140/gt.2005.9.1539

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

Primary: 20F67

Secondary: 20F55, 20F65

References

Publication

Received: 8 February 2005
Revised: 2 July 2005
Accepted: 4 August 2005
Published: 10 August 2005
Proposed: Benson Farb
Seconded: David Gabai, Martin Bridson

Authors