Higher Arf Functions and Topology of the Moduli Space of Higher Spin Riemann Surfaces
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.
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
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