Symplectic Lefschetz fibrations on S1 × M3
Symplectic Lefschetz fibrations on S1 × M3
复制标题
S1 × M3 上的辛 Lefschetz 纤维
DOI：
10.2140/gt.2000.4.517
复制
发表时间：
2000
影响因子：
2
通讯作者：
R. Matveyev
中科院分区：
文献类型：
--
作者：
Weimin Chen;R. Matveyev
在本文中，我们分类辛Lefschetz纤维化（空基轨迹）上的四个流形，这是一个产品的三个流形与一个圆。这个结果提供了进一步的证据来支持以下关于这样的四维流形上的辛结构的猜想：如果一个三流形与一个圆的乘积允许一个辛结构，那么这个三流形必须在一个圆上纤维化，直到这个四流形的一个自同构，辛结构是与由三流形在圆上的纤维化确定的规范辛结构等效的变形。
In this paper we classify symplectic Lefschetz fibrations (with empty base locus) on a four-manifold which is the product of a three-manifold with a circle. This result provides further evidence in support of the following conjecture regarding symplectic structures on such a four-manifold: if the product of a three-manifold with a circle admits a symplectic structure, then the three-manifold must fiber over a circle, and up to a self-diffeomorphism of the four-manifold, the symplectic structure is deformation equivalent to the canonical symplectic structure determined by the fibration of the three-manifold over the circle.