Higher Spin Klein Surfaces

(2015) Higher Spin Klein Surfaces. Moscow Mathematical Journal. (In Press)

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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
Depositing User: Symplectic Admin
Date Deposited: 23 Jul 2015 10:11
Last Modified: 11 Apr 2016 08:50
URI: http://livrepository.liverpool.ac.uk/id/eprint/2017104

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