HIGHER SPIN KLEIN SURFACES


Natanzon, Sergey and Pratoussevitch, Anna ORCID: 0000-0003-2248-6382 (2016) HIGHER SPIN KLEIN SURFACES. MOSCOW MATHEMATICAL JOURNAL, 16 (1). pp. 95-124.

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Abstract

We find all m-spin structures on Klein surfaces of genus larger than one. An m-spin structure on a Riemann surface P is a complex line bundle on P whose m-th tensor power is the cotangent bundle of P. A Klein surface can be described by a pair (P,tau), where P is a Riemann surface and tau is an anti-holomorphic involution on P. An m-spin structure on a Klein surface (P,tau) is an m-spin structure on the Riemann surface P which is preserved under the action of the anti-holomorphic involution tau. We determine the conditions for the existence and give a complete description of all real m-spin structures on a Klein surface. In particular, we compute the number of m-spin structures on a Klein surface (P,tau) in terms of its natural topological invariants.

Item Type: Article
Additional Information: v3: minor corrections; v2: 29 pages, 4 figures; typos corrected, Theorems 4.3 and 4.4 rephrased
Uncontrolled Keywords: Higher spin bundles, higher Theta characteristics, real forms, Riemann surfaces, Klein surfaces, Arf functions, lifts of Fuchsian groups
Depositing User: Symplectic Admin
Date Deposited: 21 Apr 2016 15:17
Last Modified: 16 Dec 2022 01:47
DOI: 10.17323/1609-4514-2016-16-1-95-124
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3000466

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