Acta Mathematica

Cone metrics on the sphere and Livné’s lattices

John R. Parker

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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.

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Acta Math., Volume 196, Number 1 (2006), 1-64.

Received: 20 May 2005
Revised: 21 October 2005
First available in Project Euclid: 31 January 2017

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2006 © Springer-Verlag


Parker, John R. Cone metrics on the sphere and Livné’s lattices. Acta Math. 196 (2006), no. 1, 1--64. doi:10.1007/s11511-006-0001-9.

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