Uniqueness of Real Lagrangians up to Cobordism

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 i...

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Bibliographic Details
Published in:International mathematics research notices 2021-04, Vol.2021 (8), p.6184-6199
Main Author: Kim, Joontae
Format: Article
Language:English
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Summary: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 antidiagonal sphere or Lagrangian isotopic to the Clifford torus.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnz345