Ricci flow and contractibility of spaces of metrics

Richard H. Bamler; Bruce Kleiner

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arXiv · 1909.08710

Ricci flow and contractibility of spaces of metrics

Richard H. Bamler·Bruce Kleiner

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Abstract

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

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Richard H. Bamler, Bruce Kleiner. 2019-09-18. Ricci flow and contractibility of spaces of metrics. https://arxiv.org/abs/1909.08710

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