Ricci flow on open 3-manifolds and positive scalar curvature

Abstract

We show that an orientable 3-dimensional manifold M admits a complete riemannian metric of bounded geometry and uniformly pos- itive scalar curvature if and only if there exists a finite collection F of spherical space-forms such that M is a (possibly infinite) connected sum where each summand is diffeomorphic to S2xS1 or to some mem- ber of F. This result generalises G. Perelman's classification theorem for compact 3-manifolds of positive scalar curvature. The main tool is a variant of Perelman's surgery construction for Ricci flow.

65 pages

References in corpus (7)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Ricci Flow and the Poincare Conjecture
• Ricci flow of non-collapsed 3-manifolds whose Ricci curvature is bounded from below
• Some open 3-manifolds and 3-orbifolds without locally finite canonical decompositions
• Complete 4-manifolds with uniformly positive isotropic curvature
• Complete classification of compact four-manifolds with positive isotropic curvature

Cited by in corpus (7)

• Ricci flow on asymptotically Euclidean manifolds
• Complete 4-manifolds with uniformly positive isotropic curvature
• Producing 3d Ricci flows with non-negative Ricci curvature via singular Ricci flows
• Compact manifolds of dimension $n\ge 12$ with positive isotropic curvature
• Ricci flow on open 4-manifolds with positive isotropic curvature
• Topological Rigidity and Positive scalar curvature
• Open 3-manifolds which are connected sums of closed ones