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Journal of Differential Geometry 58 (2001), 113-149.

The Smale Conjecture for hyperbolic 3-manifolds: Isom(M3) "\simeq" Diff(M3)

David Gabai

Abstract:

The main result of this paper is, ``If $M$ is a closed hyperbolic 3-manifold, then the inclusion of the isometry group Isom$(M)$ into the diffeomorphism group Diff$(M)$ is a homotopy equivalence."