A better proof of the Goldman–Parker conjecture

Schwartz, Richard Evan

doi:10.2140/gt.2005.9.1539

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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 2000

Primary: 20F67

Secondary: 20F65, 20F55

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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/

Volume 9, issue 3 (2005)