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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060

A better proof of the Goldman–Parker conjecture

Richard Evan Schwartz

Geometry & Topology 9 (2005) 1539–1601

DOI: 10.2140/gt.2005.9.1539

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

Primary: 20F67

Secondary: 20F55, 20F65

References
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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
Richard Evan Schwartz
Department of Mathematics
University of Maryland
College Park
Maryland 20742
USA
http://www.math.brown.edu/~res/