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arXiv · 1902.01302

Uniqueness of real Lagrangians up to cobordism

Joontae Kim
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Abstract

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.

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Joontae Kim. 2020-03-18. Uniqueness of real Lagrangians up to cobordism. https://doi.org/10.1093/imrn%2Frnz345

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