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2011 Ricci flow on open $3$–manifolds and positive scalar curvature
Laurent Bessières, Gérard Besson, Sylvain Maillot
Geom. Topol. 15(2): 927-975 (2011). DOI: 10.2140/gt.2011.15.927

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.

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Laurent Bessières. Gérard Besson. Sylvain Maillot. "Ricci flow on open $3$–manifolds and positive scalar curvature." Geom. Topol. 15 (2) 927 - 975, 2011. https://doi.org/10.2140/gt.2011.15.927

Information

Received: 10 February 2010; Revised: 25 March 2011; Accepted: 8 May 2011; Published: 2011
First available in Project Euclid: 20 December 2017

zbMATH: 1237.53064
MathSciNet: MR2821567
Digital Object Identifier: 10.2140/gt.2011.15.927

Subjects:
Primary: 53C21 , 53C44 , 57M50

Keywords: Ricci flow , three-dimensional topology

Rights: Copyright © 2011 Mathematical Sciences Publishers

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Vol.15 • No. 2 • 2011
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