Symplectic llings and positive scalar curvature
Symplectic llings and positive scalar curvature
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辛填充和正标量曲率
DOI：
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发表时间：
1998
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通讯作者：
P. Lisca
中科院分区：
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作者：
P. Lisca
设X是具有接触边界的4{流形。我们证明了Kronheimer和Mrowka引入的X的单极不变量在下列条件下为零：(I)X边界的连通分支具有正的标量曲率度量；(Ii)b+(X)>；0或X的边界是不连通的。作为应用，我们证明了Poincar e同调3{球，定向为正E8管道的边界，不具有辛半音节接触结构。特别地，这证明了Gompf的一个猜想，并提供了3{流形不是辛半音节的第一个例子。利用Fryhov的工作，我们还证明了一个约束有理同调3{球面具有正标量曲率度量的辛映射的拓扑的结果。
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 b + (X) > 0 or the boundary of X is disconnected. As an application we show that the Poincar e homology 3{sphere, oriented as the boundary of the positive E8 plumbing, does not carry symplectically semi-llable contact structures. This proves, in particular, a conjecture of Gompf, and provides the rst example of a 3{manifold which is not symplectically semi-llable. Using work of Fryshov, we also prove a result constraining the topology of symplectic llings of rational homology 3{spheres having positive scalar curvature metrics.