Diffeomorphism groups of prime 3-manifolds.

Let X be a compact orientable non-Haken 3-manifold modeled on the Thurston geometry Nil . We show that the diffeomorphism group Diff ⁡ (X) deformation retracts to the isometry group Isom ⁡ (X) . Combining this with earlier work by many authors, this completes the determination the homotopy type of Diff ⁡ (X) for any compact, orientable, prime 3-manifold X. [ABSTRACT FROM AUTHOR]