CONVEX DECOMPOSITIONS OF REAL PROJECTIVE SURFACES .2. ADMISSIBLE DECOMPOSITIONS

A real projective surface is a differentiable surface with an atlas of charts to real projective plane RP(2) such that transition functions are restrictions of projective automorphisms of RP(2). Let Sigma be an orientable compact real projective surface with convex boundary and negative Euler characteristic. Then Sigma uniquely decomposes along mutually disjoint imbedded closed projective geodesics into compact subsurfaces that are maximal annuli, trivial annuli, or maximal purely convex real projective surfaces. This is a positive answer to a question by Thurston and Goldman raised around 1977.