Mostow's lattices and cone metrics on the sphere

Boadi, Richard K; Parker, John R

Abstract

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.

Citation

Boadi, R. K., & Parker, J. R. (2015). Mostow's lattices and cone metrics on the sphere. Advances in Geometry, 15(1), 27-53. https://doi.org/10.1515/advgeom-2014-0022

• Journal Article Type: Article
• Publication Date: Jan 14, 2015
• Deposit Date: Nov 3, 2014
• Publicly Available Date: Nov 3, 2014
• Journal: Advances in Geometry
• Print ISSN: 1615-715X
• Electronic ISSN: 1615-7168
• Publisher: De Gruyter
• Peer Reviewed: Peer Reviewed
• Volume: 15
• Issue: 1
• Pages: 27-53
• DOI: https://doi.org/10.1515/advgeom-2014-0022
• Keywords: Contact manifold, Null geodesic, Space of geodesics, Billiards.
• Public URL: https://durham-repository.worktribe.com/output/1420687