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

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

2004-11-17

arxiv.org/abs/math/0411375v6

Journal of Lie Theory 19 (2009), 107-148.

Mathematics

Algebraic Geometry

32 pages, 6 figures; v3: exposition improved, typos corrected; v4: Lemma 3.9 corrected; v5: small changes in Def. 4.2 and proo

Scientific paper

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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