Geometry & Topology
- Geom. Topol.
- Volume 2, Number 1 (1998), 103-116.
Symplectic fillings and positive scalar curvature
Let be a 4–manifold with contact boundary. We prove that the monopole invariants of introduced by Kronheimer and Mrowka vanish under the following assumptions: (i) a connected component of the boundary of carries a metric with positive scalar curvature and (ii) either or the boundary of is disconnected. As an application we show that the Poincaré homology 3–sphere, oriented as the boundary of the positive 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.
Geom. Topol., Volume 2, Number 1 (1998), 103-116.
Received: 27 February 1998
Accepted: 9 July 1998
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
Secondary: 57M50: Geometric structures on low-dimensional manifolds 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]
Lisca, Paolo. Symplectic fillings and positive scalar curvature. Geom. Topol. 2 (1998), no. 1, 103--116. doi:10.2140/gt.1998.2.103. https://projecteuclid.org/euclid.gt/1513882904