Ricci flow and contractibility of spaces of metrics

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.

arXiv comment111 pages

References in corpus (2)

• Evolution of curves and surfaces by mean curvature
• Long-time behavior of 3 dimensional Ricci flow -- Introduction

Cited by in corpus (9)

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• Minimal $2$-Spheres and Optimal Foliations in $3$-Spheres with Arbitrary Metric
• A Note about Isotopy and Concordance of Positive Scalar Curvature Metrics on Compact Manifolds with Boundary
• Equivariant $3$-manifolds with positive scalar curvature