McCullen, Curtis T. 2015. The Gauss–Bonnet theorem for cone manifolds and volumes of moduli spaces. Working Paper, Harvard University.
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 M0,n with respect to the complex hyperbolic metrics introduced by Picard, Deligne–Mostow and Thurston.