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July 2006 Smooth s-Cobordisms of Elliptic 3-Manifolds
Weimin Chen
J. Differential Geom. 73(3): 413-490 (July 2006). DOI: 10.4310/jdg/1146169935

Abstract

The main result of this paper states that a symplectic s-cobordism of elliptic 3-manifolds is diffeomorphic to a product (assuming a canonical contact structure on the boundary). Based on this theorem, we conjecture that a smooth s-cobordism of elliptic 3-manifolds is smoothly a product if its universal cover is smoothly a product. We explain how the conjecture fits naturally into the program of Taubes of constructing symplectic structures on an oriented smooth 4-manifold with b+2 ≥ 1 from generic self-dual harmonic forms. The paper also contains an auxiliary result of independent interest, which generalizes Taubes' theorem "SW ⇒ Gr" to the case of symplectic 4-orbifolds.

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Weimin Chen. "Smooth s-Cobordisms of Elliptic 3-Manifolds." J. Differential Geom. 73 (3) 413 - 490, July 2006. https://doi.org/10.4310/jdg/1146169935

Information

Published: July 2006
First available in Project Euclid: 27 April 2006

zbMATH: 1099.53055
MathSciNet: MR2228319
Digital Object Identifier: 10.4310/jdg/1146169935

Rights: Copyright © 2006 Lehigh University

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Vol.73 • No. 3 • July 2006
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