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

Natanzon, Sergey and Pratoussevitch, Anna ORCID: 0000-0003-2248-6382 Higher Arf Functions and Topology of the Moduli Space of Higher Spin Riemann Surfaces. Journal of Lie Theory 19 (2009), 107-148..

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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.

Item Type:	Article
Additional Information:	32 pages, 6 figures; v3: exposition improved, typos corrected; v4: Lemma 3.9 corrected; v5: small changes in Def. 4.2 and proof of Lemma 4.5
Uncontrolled Keywords:	math.AG, math.AG, math.GT, 14J60, 30F10 (Primary); 14J17 (Secondary)
Depositing User:	Symplectic Admin
Date Deposited:	11 Apr 2016 16:10
Last Modified:	12 Nov 2019 14:35
Related URLs:	Author
URI:	http://livrepository.liverpool.ac.uk/id/eprint/3000213

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