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1998 Symplectic fillings and positive scalar curvature
Paolo Lisca
Geom. Topol. 2(1): 103-116 (1998). DOI: 10.2140/gt.1998.2.103

Abstract

Let X be a 4–manifold with contact boundary. We prove that the monopole invariants of X introduced by Kronheimer and Mrowka vanish under the following assumptions: (i) a connected component of the boundary of X carries a metric with positive scalar curvature and (ii) either b2+(X)>0 or the boundary of X is disconnected. As an application we show that the Poincaré homology 3–sphere, oriented as the boundary of the positive E8 plumbing, does not carry symplectically semi-fillable contact structures. This proves, in particular, a conjecture of Gompf, and provides the first example of a 3–manifold which is not symplectically semi-fillable. Using work of Frøyshov, we also prove a result constraining the topology of symplectic fillings of rational homology 3–spheres having positive scalar curvature metrics.

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Paolo Lisca. "Symplectic fillings and positive scalar curvature." Geom. Topol. 2 (1) 103 - 116, 1998. https://doi.org/10.2140/gt.1998.2.103

Information

Received: 27 February 1998; Accepted: 9 July 1998; Published: 1998
First available in Project Euclid: 21 December 2017

zbMATH: 0942.53050
MathSciNet: MR1633282
Digital Object Identifier: 10.2140/gt.1998.2.103

Subjects:
Primary: 53C15
Secondary: 57M50, 57R57

Rights: Copyright © 1998 Mathematical Sciences Publishers

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