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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Ricci flow on open $3$–manifolds and positive scalar curvature

Laurent Bessières, Gérard Besson and Sylvain Maillot

Geometry & Topology 15 (2011) 927–975
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 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 . 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.

Keywords
Ricci flow, three-dimensional topology
Mathematical Subject Classification 2000
Primary: 53C21, 53C44, 57M50
References
Publication
Received: 10 February 2010
Revised: 25 March 2011
Accepted: 8 May 2011
Published: 18 June 2011
Proposed: David Gabai
Seconded: Peter Teichner, Gang Tian
Authors
Laurent Bessières
Institut Fourier
UMR CNRS 5582 Université de Grenoble I
BP 74
100 rue des maths
38402 Saint Martin d’Hères
France
http://www-fourier.ujf-grenoble.fr/~lbessier/
Gérard Besson
Institut Fourier
UMR CNRS 5582 Université de Grenoble I
BP 74
100 rue des maths
38402 Saint Martin d’Hères
France
http://www-fourier.ujf-grenoble.fr/~besson/
Sylvain Maillot
Institut de Mathématiques et de Modélisation de Montpellier (I3M)
UMR CNRS 5149 Université Montpellier 2
Case Courrier 051
Place Eugène Bataillon
34095 Montpellier
France
http://www.math.univ-montp2.fr/~maillot/