RICCI FLOW AND DIFFEOMORPHISM GROUPS OF 3-MANIFOLDS

We complete the proof of the Generalized Smale Conjecture, apart from the case of RP3, and give a new proof of Gabai’s theorem for hyperbolic 3-manifolds. We use an approach based on Ricci flow through singularities, which applies uniformly to spherical space forms, except S3 and RP3, as well as hyperbolic manifolds, to prove that the space of metrics of constant sectional curvature is contractible. As a corollary, for such a 3-manifold X, the inclusion Isom (formula presented) is a homotopy equivalence for any Riemannian metric g of constant sectional curvature.