Ricci flow on open 3-manifolds and positive scalar curvature

Details Ricci flow on open 3-manifolds and positive scalar curvature Ricci flow on open 3-manifolds and positive scalar curvature

2010-01-09

arxiv.org/abs/1001.1458v1

Mathematics

Differential Geometry

65 pages

Scientific paper

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.

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