Cone metrics on the sphere and Livne's lattices

Parker, John R.

Abstract

We give an explicit construction of a family of lattices in PU (1, 2) originally constructed by Livné. Following Thurston, we construct these lattices as the modular group of certain Euclidean cone metrics on the sphere. We give connections between these groups and other groups of complex hyperbolic isometries.

Citation

Parker, J. R. (2006). Cone metrics on the sphere and Livne's lattices. Acta Mathematica, 196(1), 1-64. https://doi.org/10.1007/s11511-006-0001-9

• Journal Article Type: Article
• Publication Date: 2006-07
• Deposit Date: Mar 27, 2008
• Journal: Acta Mathematica
• Print ISSN: 0001-5962
• Electronic ISSN: 1871-2509
• Publisher: Institut Mittag-Leffler
• Peer Reviewed: Peer Reviewed
• Volume: 196
• Issue: 1
• Pages: 1-64
• DOI: https://doi.org/10.1007/s11511-006-0001-9
• Public URL: https://durham-repository.worktribe.com/output/1562831
• Publisher URL: http://www.springerlink.com/content/u01j290tl8379751/