Mostow's lattices and cone metrics on the sphere

Boadi, Richard K; Parker, John R

doi:10.1515/advgeom-2014-0022

Mostow's lattices and cone metrics on the sphere

Boadi, Richard K; Parker, John R

Authors

Richard K Boadi

Professor John Parker j.r.parker@durham.ac.uk
Professor

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.