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Higher Arf Functions and Topology of the Moduli Space of Higher Spin Riemann Surfaces

Sergey Natanzon·Anna Pratoussevitch
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Abstract

We prove that any connected component of the space of m-spin structures on compact Riemann surfaces with finite number of punctures and holes is homeomorphic to a quotient of the vector space R^d by a discrete group action. Our proof is based on the representation of the space of m-spin structures on a Riemann surface as a finite affine space of Z/mZ-valued functions on the fundamental group of the surface.

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Sergey Natanzon, Anna Pratoussevitch. 2009-05-18. Higher Arf Functions and Topology of the Moduli Space of Higher Spin Riemann Surfaces. https://arxiv.org/abs/math/0411375

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