Classification of m -spin Klein surfaces

A Klein surface is a generalisation of a Riemann surface to the case of non-orientable surfaces and/or surfaces with boundary [1], [4]. A Klein surface is a quotient P/[tau], where [tau]:P arrow right P is an anti-holomorphic involution of a Riemann surface P. The category of Klein surfaces is isomorphic to the category of real algebraic curves. A complete list of topological invariants of a connected Klein surface P/[tau] consists of the (algebraic) genus g= g(P), the number k=k(P/[tau]) = [partialdifferential](P/[tau]) of ovals, and the orientability[varepsilon] = [varepsilon](P/[tau]). An oval is a connected component of the boundary [partialdifferential](P/[tau]).