Notes on complex hyperbolic triangle groups

Kamiya, Shigeyasu; Parker, John R.; Thompson, James M.

Abstract

We first demonstrate a family of isomorphisms between complex hyperbolic triangle groups and outline a systematic approach classifying the groups. Then we describe conditions that determine the discreteness of certain groups, in particular we prove a slightly weaker version of a conjecture given by Schwartz. Finally we collect together a list of known discrete triangle groups and propose some good candidates for discrete groups.

Citation

Kamiya, S., Parker, J. R., & Thompson, J. M. (2010). Notes on complex hyperbolic triangle groups. Conformal Geometry and Dynamics, 14, 202-218. https://doi.org/10.1090/s1088-4173-2010-00215-8

• Journal Article Type: Article
• Publication Date: Jan 1, 2010
• Deposit Date: Nov 19, 2010
• Publicly Available Date: Dec 6, 2010
• Journal: Conformal Geometry and Dynamics
• Print ISSN: 1088-4173
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 14
• Pages: 202-218
• DOI: https://doi.org/10.1090/s1088-4173-2010-00215-8