On an exotic Lagrangian torus in $\mathbb{C}{P}^2$

Abstract

We find a non-displaceable Lagrangian torus fiber in a semi-toric system, which is superheavy with respect to certain symplectic quasi-state. In particular, this proves Lagrangian $\RR P^2$ is not a stem in $\CC P^2$, answering a question of Entov and Polterovich.

Largely modified on the second version. Comments welcome

References in corpus (2)

• Lagrangian spheres, symplectic surfaces and the symplectic mapping class group
• Lagrangian spheres in Del Pezzo surfaces

Cited by in corpus (3)

• Infinitely many exotic monotone Lagrangian tori in CP^2
• On Certain Lagrangian Submanifolds of $S^2\times S^2$ and $C{P}^n$
• $A_n$-type surface singularity and nondisplaceable Lagrangian tori