Hamiltonian unknottedness of certain monotone Lagrangian tori in $S^2\times S^2$

TL;DR

This paper proves that certain monotone Lagrangian tori in the symplectic manifold $S^2 imes S^2$ are Hamiltonian isotopic to the Clifford torus, under specific geometric conditions involving symplectic fibrations.

Contribution

It establishes a Hamiltonian unknottedness result for a class of monotone Lagrangian tori in $S^2 imes S^2$, linking their topology to the Clifford torus.

Findings

Monotone Lagrangian tori with specific fibration properties are Hamiltonian isotopic to the Clifford torus.

The result applies to tori sitting in symplectic fibrations with two sections in their complement.

Provides new insights into the classification of Lagrangian tori in symplectic geometry.

Abstract

We prove that a monotone Lagrangian torus in $S^2\times S^2$ which suitably sits in a symplectic fibration with two sections in its complement is Hamiltonian isotopic to the Clifford torus.