Ricci flow and contractibility of spaces of metrics

By Richard Bamler, Bruce Kleiner. 2019

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Author(s): Bamler, Richard H; Kleiner, Bruce | 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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8aac3fb0fbae919ce9e45bbd23ab35c9630f064d