On exotic monotone Lagrangian tori in $\mathbb{C}P^2$ and $S^2 \times S^2$

TL;DR

This paper proves that two different constructions of exotic monotone Lagrangian tori in complex projective plane and product of spheres are Hamiltonian isotopic, unifying previously distinct examples in symplectic geometry.

Contribution

It demonstrates that the Chekanov-Schlenk and Biran circle bundle constructions produce Hamiltonian isotopic tori in specific symplectic manifolds.

Findings

The two constructions yield Hamiltonian isotopic tori in $\

$ ext{CP}^2$ and $S^2 imes S^2$.

Unification of previously distinct exotic monotone Lagrangian tori examples.

Abstract

In this note, we prove that two constructions of exotic monotone Lagrangian tori, namely the one by Chekanov and Schlenk and the one obtained by the circle bundle construction of Biran are Hamiltonian isotopic in $\mathbb{C}P^2$ and $S^2 \times S^2$.