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  1. Abstract LetXbe acompact orientable non-Haken 3-manifold modeled on the Thurston geometry Nil {\operatorname{Nil}}. We show that the diffeomorphism group Diff ( X ) {\operatorname{Diff}(X)}deformation retracts to the isometry group Isom ( X ) {\operatorname{Isom}(X)}. Combining this with earlier work by many authors, this completes the determination the homotopy type of Diff ( X ) {\operatorname{Diff}(X)}for any compact, orientable, prime 3-manifoldX. 
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