CONVEX REAL PROJECTIVE-STRUCTURES ON CLOSED SURFACES ARE CLOSED

Abstract

The deformation space c(SIGMA) of convex RP2- structures on a closed surface SIGMA with CHI(SIGMA) < 0 is closed in the space Hom(pi, SL(3, R))/SL(3, R) of equivalence classes of representations pi1(SIGMA) --> SL(3, R). Using this fact, we prove Hitchin's conjecture that the contractible ''Teichmuller component'' (Lie groups and Teichmuller space, preprint) of Hom(pi, SL(3, R))/SL(3, R) precisely equals c(SIGMA).