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Uniqueness of Real Lagrangians up to Cobordism
International Mathematics Research Notices ( IF 0.9 ) Pub Date : 2020-01-08 , DOI: 10.1093/imrn/rnz345
Joontae Kim 1
Affiliation  

We prove that a real Lagrangian submanifold in a closed symplectic manifold is unique up to cobordism. We then discuss the classification of real Lagrangians in $\mathbb{C} P^2$ and $S^2\times S^2$. In particular, we show that a real Lagrangian in $\mathbb{C} P^2$ is unique up to Hamiltonian isotopy and that a real Lagrangian in $S^2\times S^2$ is either Hamiltonian isotopic to the antidialgonal sphere or Lagrangian isotopic to the Clifford torus.

中文翻译:

直到 Cobordism 的实拉格朗日函数的唯一性

我们证明了闭辛流形中的实拉格朗日子流形对于协边是唯一的。然后我们讨论 $\mathbb{C} P^2$ 和 $S^2\times S^2$ 中实拉格朗日量的分类。特别是,我们证明 $\mathbb{C} P^2$ 中的实拉格朗日量在哈密顿量同位素范围内是唯一的,而 $S^2\times S^2$ 中的实数拉格朗日量是对角球面的哈密顿量同位素或克利福德环面的拉格朗日同位素。
更新日期:2020-01-08
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