CONVEX DECOMPOSITIONS OF REAL PROJECTIVE SURFACES .1. PI-ANNULI AND CONVEXITY

Abstract

A real projective surface is a surface with a flat real projective structure. A pi-annulus is an easy-to-construct real projective annulus with geodesic boundary. Let SIGMA be an orientable compact real projective surface with convex boundary and negative Euler characteristic. We prove that there is a pi-annulus with a projective map to SIGMA whenever SIGMA is not convex.