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Ricci flow on open
$3$–manifolds and positive scalar curvature
Laurent Bessières, Gérard Besson and Sylvain Maillot |
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Geometry & Topology 15 (2011) 927–975
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Abstract |
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We show that an orientable –dimensional manifold 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 is a (possibly infinite) connected sum where each summand is diffeomorphic to or to some member of . This result generalises G Perelman’s classification theorem for compact –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
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Mathematical Subject Classification 2000
Primary: 53C21, 53C44, 57M50
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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
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Authors |
| Laurent Bessières | |
| Institut Fourier UMR CNRS 5582 Université de Grenoble I BP 74 100 rue des maths 38402 Saint Martin d’Hères France |
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| 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 |
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| 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 |
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| http://www.math.univ-montp2.fr/~maillot/ | |
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