Unlinking and unknottedness of monotone Lagrangian submanifolds
Unlinking and unknottedness of monotone Lagrangian submanifolds
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单调拉格朗日子流形的解链和无结性
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发表时间：
2012
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通讯作者：
J. Evans
中科院分区：
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作者：
Georgios Dimitroglou Rizell;J. Evans
在一定的拓扑假设下，我们证明了嵌入在标准辛向量空间中具有相同单调常数的两个单调拉格朗日子流形不能相互连接，并且单独地，它们的光滑结类型完全由分类下面的拉格朗日浸没的同伦理论数据决定。拓扑假设由一大类实现为单调拉格朗日的流形来满足，包括环面。通过一些额外的同伦理论计算，我们推导出奇数复维至少为5的辛向量空间中所有单调拉格朗日环面都是光滑同位素。53 d12
Under certain topological assumptions, we show that two monotone Lagrangian submanifolds embedded in the standard symplectic vector space with the same monotonicity constant cannot link one another and that, individually, their smooth knot type is determined entirely by the homotopy theoretic data which classifies the underlying Lagrangian immersion. The topological assumptions are satisfied by a large class of manifolds which are realised as monotone Lagrangians, including tori. After some additional homotopy theoretic calculations, we deduce that all monotone Lagrangian tori in the symplectic vector space of odd complex dimension at least five are smoothly isotopic. 53D12