Unknottedness of real Lagrangian tori in $S^2\times S^2$

Abstract

We prove the Hamiltonian unknottedness of real Lagrangian tori in the monotone $S^2\times S^2$, namely any real Lagrangian torus in $S^2\times S^2$ is Hamiltonian isotopic to the Clifford torus $\mathbb{T}_{\text{Clif}}$. The proof is based on a neck-stretching argument, Gromov's foliation theorem, and the Cieliebak-Schwingenheuer criterion.