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Ricci flow and contractibility of spaces of metrics

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arxiv 1909.08710 v1 pith:N6BYQVPC submitted 2019-09-18 math.DG math.APmath.GT

Ricci flow and contractibility of spaces of metrics

classification math.DG math.APmath.GT
keywords casegroupmetricsspaceargumentconjecturecontractibilitycontractible
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric

    math.DG 2026-07 accept novelty 7.0

    Every Riemannian manifold diffeomorphic to S^{3} contains at least two distinct embedded minimal 2-spheres.

  2. Relative eta invariant and uniformly positive scalar curvature on non-compact manifolds

    math.DG 2024-02 unverdicted novelty 6.0

    Introduces relative eta invariants for Dirac operators coinciding at infinity on non-compact manifolds with bounded curvature, yielding a spectral flow formula, a new proof of a Gromov-Lawson result, and an APS index ...

  3. Mean Curvature Flow and Heegaard Surfaces in Lens Spaces

    math.DG 2023-12 unverdicted novelty 6.0

    The moduli space of mean convex two-spheres in complete orientable 3-manifolds with nonnegative Ricci curvature is path-connected; mean convex Heegaard tori have one or two path components depending on a precise chara...