Unlinking and unknottedness of monotone Lagrangian submanifolds

Dimitroglou Rizell, Georgios and Evans, Jonathan David (2014) Unlinking and unknottedness of monotone Lagrangian submanifolds. Geometry and Topology, 18 (2). pp. 997-1034. ISSN 1364-0380

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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.

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Journal Article
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Geometry and Topology
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02 Apr 2019 10:50
Last Modified:
26 Jan 2023 01:52