THE CLASSIFICATION OF REAL PROJECTIVE-STRUCTURES ON COMPACT SURFACES

Real projective structures (RP2-structures) on compact surfaces are cl assified. The space of projective equivalence classes of real projecti ve structures on a closed orientable surface of genus g > 1 is a count able disjoint union of open cells of dimension 16g - 16. A key idea is Choi's admissible decomposition of a real projective structure into c onvex subsurfaces along closed geodesics. The deformation space of con vex structures forms a connected component in the moduli space of repr esentations of the fundamental group in PGL(3, R), establishing a conj ecture of Hitchin.