A better proof of the Goldman–Parker conjecture

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.