## Geometry & Topology

### 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 positive 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 member 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.

#### Article information

Source
Geom. Topol., Volume 15, Number 2 (2011), 927-975.

Dates
Revised: 25 March 2011
Accepted: 8 May 2011
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732308

Digital Object Identifier
doi:10.2140/gt.2011.15.927

Mathematical Reviews number (MathSciNet)
MR2821567

Zentralblatt MATH identifier
1237.53064

#### Citation

Bessières, Laurent; Besson, Gérard; Maillot, Sylvain. Ricci flow on open $3$–manifolds and positive scalar curvature. Geom. Topol. 15 (2011), no. 2, 927--975. doi:10.2140/gt.2011.15.927. https://projecteuclid.org/euclid.gt/1513732308

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