Deligne-Mostow lattices with three fold symmetry and cone metrics on the sphere

Pasquinelli, Irene

Abstract

Deligne and Mostow constructed a class of lattices in $ PU(2,1)$ using monodromy of hypergeometric functions. Thurston reinterpreted them in terms of cone metrics on the sphere. In this spirit we construct a fundamental domain for the lattices with three fold symmetry in the list of Deligne and Mostow. This is a generalisation of the works of Boadi and Parker and gives a different interpretation of the fundamental domain constructed by Deraux, Falbel, and Paupert.

Citation

Pasquinelli, I. (2016). Deligne-Mostow lattices with three fold symmetry and cone metrics on the sphere. Conformal Geometry and Dynamics, 20(12), 235-281. https://doi.org/10.1090/ecgd/299

• Journal Article Type: Article
• Acceptance Date: May 15, 2016
• Online Publication Date: Jul 19, 2016
• Publication Date: Jul 19, 2016
• Deposit Date: May 25, 2016
• Publicly Available Date: Sep 14, 2016
• Journal: Conformal Geometry and Dynamics
• Print ISSN: 1088-4173
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 20
• Issue: 12
• Pages: 235-281
• DOI: https://doi.org/10.1090/ecgd/299
• Related Public URLs: https://arxiv.org/abs/1509.05320