Hyperbolic 2-spheres with cone singularities

Author(s)

Anan'in, Sasha ^[1] ; Grossi, Carlos H. ^[1] ; Lee, Jaejeong ^[2] ; dos Reis Jr, Joao

Affiliation

^[1] Univ Sao Paulo, Dept Matemat, ICMC, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

^[2] KIAS, 85 Hoegiro, Seoul 02455 - South Korea

• Document type: Journal article
• Source: Topology and its Applications; v. 272, MAR 1 2020.
• Web of Science Citations: 0

Abstract

We study the space C(a(0), a(1), ..., a(n)) of hyperbolic 2-spheres with cone points of prescribed apex curvatures 2a(0), 2a(1), ..., 2a(n) is an element of]0, 2 pi{[} and some related spaces. For n = 3, we get a detailed description of such spaces. The euclidean 2-spheres were considered by W. P. Thurston: for n = 4, the corresponding spaces provide the famous 7 examples of nonarithmetic compact holomorphic 2-ball quotients previously constructed by Deligne-Mostow. (C) 2020 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 15/25809-2 - Algebraic geometry, dynamics, and hyperbolic geometry
• Grantee: Alexandre Ananin
• Support Opportunities: Regular Research Grants
• FAPESP's process: 14/26295-0 - New manifolds modelled on the holomorphic 2-ball
• Grantee: João dos Reis Junior
• Support Opportunities: Scholarships in Brazil - Scientific Initiation