Spin Graphs

Abstract

We show that on any Riemann surface S of genus g>1 any nonsingular even spin bundle defines e-foloation of S. When a surface is hyperelliptic then all leaves of this foliation are finite and almost all of them consists of 2g+2 points. Moreover, each leaf carries an additional structure which allows us to view it as a concrete graph. We find the properties of these spin graphs and we describe the classification of surfaces which is given by these properties. The classification is based on a finite genus g>1.number of exceptional graphs which have to be present on any surface S of