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Unlinking and unknottedness of monotone Lagrangian submanifolds. (English) Zbl 1311.53065
Summary: 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.

MSC:
53D12 Lagrangian submanifolds; Maslov index
57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)
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