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Mostow's lattices and cone metrics on the sphere.

Boadi, Richard K. and Parker, John R. (2015) 'Mostow's lattices and cone metrics on the sphere.', Advances in geometry., 15 (1). pp. 27-53.


In his seminal paper of 1980, Mostow constructed a family of lattices in PU(2, 1), the holomorphic isometry group of complex hyperbolic 2-space. In this paper, we use a description of these lattices given by Thurston in terms of cone metrics on the sphere, which is equivalent to Deligne and Mostow’s description of them using monodromy of hypergeometric functions. We give an explicit fundamental domain for some of Mostow’s lattices, specifically those with large phase shift. Our approach follows Parker’s approach of describing Livné’s lattices in terms of cone metrics on the sphere. The content of this paper is based on Boadi’s PhD thesis.

Item Type:Article
Keywords:Contact manifold, Null geodesic, Space of geodesics, Billiards.
Full text:(AM) Accepted Manuscript
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Date accepted:No date available
Date deposited:03 November 2014
Date of first online publication:January 2015
Date first made open access:No date available

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