Uniqueness of real Lagrangians up to cobordism

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.

15 pages, final version, to appear IMRN

References in corpus (2)

• Lagrangian spheres, symplectic surfaces and the symplectic mapping class group
• Lagrangian isotopy of tori in $S^2\times S^2$ and $\mathbb{C}{P}^2$

Cited by in corpus (1)

• On the topology of real Lagrangians in toric symplectic manifolds