Higher Spin Klein Surfaces
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.
Keywords
Cite
@article{arxiv.1502.06546,
title = {Higher Spin Klein Surfaces},
author = {Sergey Natanzon and Anna Pratoussevitch},
journal= {arXiv preprint arXiv:1502.06546},
year = {2016}
}
Comments
v3: minor corrections; v2: 29 pages, 4 figures; typos corrected, Theorems 4.3 and 4.4 rephrased