Ricci flow on open 3-manifolds and positive scalar curvature

Laurent Bessières (1) , Gérard Besson (1) , Sylvain Maillot (2)

1 IF - Institut Fourier
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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 S2×S1 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.

Mots clés: 3-manifolds; scalar curvature; Ricci flow

Domaines: Géométrie différentielle [math.DG]; Topologie géométrique [math.GT]

Laurent Bessières, Gérard Besson, Sylvain Maillot. Ricci flow on open 3-manifolds and positive scalar curvature. Geometry and Topology, 2011, 15 (2), pp.927-975. ⟨10.2140/gt.2011.15.927⟩. ⟨hal-00445607⟩