The Gauss-Bonnet theorem for cone manifolds and volumes of moduli spaces | Zendy

Curtis T. McMullen | Zendy

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The Gauss-Bonnet theorem for cone manifolds and volumes of moduli spaces

Author(s) -

Curtis T. McMullen

Publication year - 2017

Publication title -

american journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.818

H-Index - 67

eISSN - 1080-6377

pISSN - 0002-9327

DOI - 10.1353/ajm.2017.0005

Subject(s) - mathematics , cone (formal languages) , pure mathematics , moduli space , gauss , moduli , gauss–bonnet theorem , class (philosophy) , mathematical analysis , mathematical physics , einstein , physics , algorithm , quantum mechanics , artificial intelligence , computer science

This paper generalizes the Gauss-Bonnet formula to a class of stratified spaces called Riemannian cone manifolds. As an application, we compute the volumes of the moduli spaces ${\cal M}_{0,n}$ with respect to the complex hyperbolic metrics introduced by Picard, Deligne-Mostow and Thurston.

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