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Abstract LetXbe acompact orientable non-Haken 3-manifold modeled on the Thurston geometry {\operatorname{Nil}}. We show that the diffeomorphism group {\operatorname{Diff}(X)}deformation retracts to the isometry group {\operatorname{Isom}(X)}. Combining this with earlier work by many authors, this completes the determination the homotopy type of {\operatorname{Diff}(X)}for any compact, orientable, prime 3-manifoldX.more » « less
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null (Ed.)Abstract In a recent paper, Brendle showed the uniqueness of the Bryant soliton among 3-dimensional κ-solutions.In this paper, we present an alternative proof for this fact and show that compact κ-solutions are rotationally symmetric.Our proof arose from independent work relating to our Strong Stability Theorem for singular Ricci flows.more » « less
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