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Ricci flow and diffeomorphism groups of 3-manifolds
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abstract
We complete the proof of the Generalized Smale Conjecture, apart from the case of $RP^3$, and give a new proof of Gabai's theorem for hyperbolic 3-manifolds. We use an approach based on Ricci flow through singularities, which applies uniformly to spherical space forms other than $S^3$ and $RP^3$ and hyperbolic manifolds, to prove that the moduli space of metrics of constant sectional curvature is contractible. As a corollary, for such a 3-manifold $X$, the inclusion $\text{Isom} (X,g)\to \text{Diff}(X)$ is a homotopy equivalence for any Riemannian metric $g$ of constant sectional curvature.
Forward citations
Cited by 2 Pith papers
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The Geometry of Loop Spaces III: Isometry Groups of Contact Manifolds
Proves π₁(Isom(M_p,g)) infinite for |p|≫0 in certain contact (4n+1)-manifolds via Wodzicki-Chern-Simons forms on LM_p, plus first high-dim nonvanishing Wodzicki-Pontryagin forms.
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Preserving curvature lower bounds when Ricci flowing non-smooth initial data
A survey of results on Ricci flow from non-smooth initial data, focusing on preservation of lower curvature bounds and open problems.
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