A Proof of the Smale Conjecture, Diff(S 3 ) ≃O(4)

The Smale Conjecture 9 is the assertion that the inclusion of the orthogonal group 0(4) into Diff(S3), the diffeomorphism group of the 3-sphere with the Cw topology, is a homotopy equivalence. There are many equivalent forms of this conjecture, some of which are listed in the appendix to this paper. We shall prove