Abstract
© 2016 Independent University of Moscow. A Klein surface is a generalisation of a Riemann surfaceto the case of non-orientable surfaces or surfaces with boundary. Thecategory of Klein surfaces is isomorphic to the category of real algebraiccurves. An m-spin structure on a Klein surface is a complex line bundlewhose m-th tensor power is the cotangent bundle. We describe all mspinstructures on Klein surfaces of genus greater than one and determinethe conditions for their existence. In particular we compute the numberof m-spin structures on a Klein surface in terms of its natural topologicalinvariants.
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