A Gauss-Bonnet formula for moduli spaces of Riemann surfaces

We prove a Gauss-Bonnet theorem for (finite coverings of) moduli spaces of Riemann surfaces endowed with the McMullen metric. The proof uses properties of an exhaustion of moduli spaces by compact submanifolds with corners and the Gauss-Bonnet formula of Allendoerfer and Weil for Riemannian polyhedra.