Exact Lagrangian submanifolds in simply-connected cotangent bundles
Exact Lagrangian submanifolds in simply-connected cotangent bundles
复制标题
DOI：
10.1007/s00222-007-0092-8
复制
发表时间：
2007-01
影响因子：
3.1
通讯作者：
K. Fukaya;P. Seidel;I. Smith
中科院分区：
文献类型：
--
作者：
K. Fukaya;P. Seidel;I. Smith
我们考虑余切丛中的正合拉格朗日子流形。在某些额外的限制下（余切丛的基本群的平凡性，以及拉格朗日子流形的Maslov类和第二Stiefel-Whitney类），我们证明了这样的子流形是Floer-cohomologically不可区分的零节。这意味着对它们的拓扑结构有很强的限制。一个本质上等价的结果最近被Nadler [16]独立地证明，使用不同的方法。
We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel–Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler [16], using a different approach.