Title : The Smale conjecture for lens spaces
(a joint work with Darryl McCullough and Hyam Rubinstein)
Speaker : Sungbok Hong (Korea University)
Abstract :

S. Smale proved that for the standard round 2 sphere $S^2$, the inclusion of the isometry group $O(3)$ into the diffeomorphism group Diff$(S^2)$ is a homotopy equivalence. He conjectured the analogous result holds for the 3-sphere. It was proved affirmatively by A. Hatcher. A natural extension of the Smale conjecture is that if any elliptic (Riemannian 3 manifold with positive constant curvature 1) 3-manifold $M$ then Isom $(M) \to$ Diff $(M)$ is a homotopy equivalence. We prove this conjecture confirmatively for lens spaces.

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