Deforming three-manifolds with positive scalar curvature

In this paper we prove that the moduli space of metrics with positive scalar curvature of an orientable compact three-manifold is path-connected. The proof uses the Ricci flow with surgery, the conformal method, and the connected sum construction of Gromov and Lawson. The work of Perelman on Hamilto...

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Bibliographic Details
Published in:Annals of mathematics 2012-09, Vol.176 (2), p.815-863
Main Author: Marques, Fernando Codá
Format: Article
Language:English
Subjects:
Curvature
Glues
Mathematical manifolds
Mathematical theorems
Mathematics
Riemann manifold
Rotation
Scalars
Topological theorems
Topology
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Summary:In this paper we prove that the moduli space of metrics with positive scalar curvature of an orientable compact three-manifold is path-connected. The proof uses the Ricci flow with surgery, the conformal method, and the connected sum construction of Gromov and Lawson. The work of Perelman on Hamilton's Ricci flow is fundamental. As one of the applications we prove the path-connectedness of the space of trace-free asymptotically flat solutions to the vacuum Einstein constraint equations on ℝ³.
ISSN:0003-486X
DOI:10.4007/annals.2012.176.2.3