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A Gauss–Bonnet formula for moduli spaces of Riemann surfaces

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Abstract

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.

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Acknowledgments

I would like thank C.T. McMullen for helpful correspondence.

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  1. Institute for Algebra und Geometry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

    Enrico Leuzinger

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  1. Enrico Leuzinger
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Correspondence to Enrico Leuzinger.

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Leuzinger, E. A Gauss–Bonnet formula for moduli spaces of Riemann surfaces. Geom Dedicata 180, 373–383 (2016). https://doi.org/10.1007/s10711-015-0106-4

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