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

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.

arXiv comment40 pages, 10 figures

References in corpus (10)

• Rigid subsets of symplectic manifolds
• Rigidity and uniruling for Lagrangian submanifolds
• Lagrangian spheres, symplectic surfaces and the symplectic mapping class group
• On Exotic Lagrangian Tori in CP^2
• Infinitely many exotic monotone Lagrangian tori in CP^2
• Lagrangian isotopy of tori in $S^2\times S^2$ and $\mathbb{C}{P}^2$
• A non-displacable Lagrangian torus in T^*S^2
• On Certain Lagrangian Submanifolds of $S^2\times S^2$ and $C{P}^n$
• Spherical Lagrangians via ball packings and symplectic cutting
• Lagrangian spheres in Del Pezzo surfaces

Cited by in corpus (2)

• The classification of Lagrangians nearby the Whitney immersion
• Packing Lagrangian tori