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We show that the space of metrics of positive scalar curvature on any3-manifold is either empty or contractible. Second, we show that thediffeomorphism group of every 3-dimensional spherical space form deformationretracts to its isometry group. This proves the Generalized Smale Conjecture.Our argument is independent of Hatcher's theorem in the $S^3$ case and inparticular it gives a new proof of the $S^3$ case.

Ricci flow and contractibility of spaces of metrics