Classification of Stokes Graphs of Second Order Fuchsian Differential Equations of Genus Two

Abstract

Stokes curves of second order Fuchsian dfferential equations on the Riemann sphere with a large parameter form sphere graphs, which are called Stokes graphs. Topological classification of Stokes graphs are given for the case where equations have five regular singular points. It is proved that there are exactly 25 degree sequences of sphere triangulations associated with Stokes graphs under suitable generic conditions.