Hyperbolic 2-spheres with cone singularities

We study the space C(a0,a1,…,an) of hyperbolic 2-spheres with cone points of prescribed apex curvatures 2a0,2a1,…,2an∈]0,2π[ 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 pr...

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Bibliographic Details
Published inTopology and its applications Vol. 272; p. 107073
Main Authors Anan'in, Sasha, Grossi, Carlos H., Lee, Jaejeong, dos Reis, João
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.03.2020
Subjects
Braid groups
Discrete actions
Nonarithmetic/arithmetic compact holomorphic 2-ball quotients
Spaces of spherical/hyperbolic structure with prescribed cone singularities on a 2-sphere
Nonarithmetic/arithmetic compact holomorphic 2-ball quotients
30F60
22E40
Spaces of spherical/hyperbolic structure with prescribed cone singularities on a 2-sphere
Discrete actions
Braid groups
20H10
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Summary:We study the space C(a0,a1,…,an) of hyperbolic 2-spheres with cone points of prescribed apex curvatures 2a0,2a1,…,2an∈]0,2π[ 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.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2020.107073