Unlinking and unknottedness of monotone Lagrangian submanifolds

Abstract

Under certain topological assumptions, we show that two monotone Lagrangian submanifolds embedded in the standard symplectic vector space with the same monotonicity constant cannot link one another and that, individually, their smooth knot type is determined entirely by the homotopy theoretic data which classifies the underlying Lagrangian immersion. The topological assumptions are satisfied by a large class of manifolds which are realised as monotone Lagrangians, including tori. After some additional homotopy theoretic calculations, we deduce that all monotone Lagrangian tori in the symplectic vector space of odd complex dimension at least five are smoothly isotopic.

arXiv comment36 pages + 5 page erratum. v2 updated to agree with published version and added an erratum

References in corpus (8)

• Compactness results in Symplectic Field Theory
• Relative asymptotic behavior of pseudoholomorphic half-cylinders
• Lagrangian spheres, symplectic surfaces and the symplectic mapping class group
• Mean curvature flow of monotone Lagrangian submanifolds
• On the extrinsic topology of Lagrangian submanifolds
• Lagrangian spheres in Del Pezzo surfaces
• Unlinking and unknottedness of monotone Lagrangian submanifolds
• Isotopies of high genus Lagrangian surfaces

Cited by in corpus (6)

• Lagrangian isotopy of tori in $S^2\times S^2$ and $\mathbb{C}{P}^2$
• String topology with gravitational descendants, and periods of Landau-Ginzburg potentials
• Unlinking and unknottedness of monotone Lagrangian submanifolds
• Nearby Lagrangian fibers and Whitney sphere links
• Dehn-Seidel twist, $C^0$ symplectic topology and barcodes
• Unknottedness of real Lagrangian tori in $S^2\times S^2$