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Cone metrics on the sphere and Livne's lattices

Parker, John R.



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.


Parker, J. R. (2006). Cone metrics on the sphere and Livne's lattices. Acta Mathematica, 196(1), 1-64.

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
Publisher URL