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EnglishLet 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 b_2^+(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.
| Autori interni: | |
| Autori: | LISCA P |
| Titolo: | Symplectic fillings and positive scalar curvature |
| Anno del prodotto: | 1998 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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