On the extrinsic topology of Lagrangian submanifolds
On the extrinsic topology of Lagrangian submanifolds
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拉格朗日子流形的外在拓扑
DOI：
10.1155/imrn.2005.2341
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发表时间：
2005
影响因子：
1
通讯作者：
Peter Albers
中科院分区：
文献类型：
--
作者：
Peter Albers
利用Floer同调方法研究了闭辛流形中拉格朗日子流形及其子流形的外在拓扑。第一个结果证明了可置换单调拉格朗日子流形的同调类在环境辛流形的同调中消失。结合谱不变量，我们提供了一种新的证明拉格朗日交点结果的机制，例如，在$\CP^n\乘以\CP^n$中任意两个单连通拉格朗日子流形必须相交。
We investigate the extrinsic topology of Lagrangian submanifolds and of their submanifolds in closed symplectic manifolds using Floer homological methods. The first result asserts that the homology class of a displaceable monotone Lagrangian submanifold vanishes in the homology of the ambient symplectic manifold. Combining this with spectral invariants we provide a new mechanism for proving Lagrangian intersection results e.g. entailing that any two simply connected Lagrangian submanifold in $\CP^n\times\CP^n$ must intersect.