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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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.

Item Type:
Journal Article
Journal or Publication Title:
Geometry and Topology
Subjects:
ID Code:
132433
Deposited By:
Deposited On:
02 Apr 2019 10:50
Refereed?:
Yes
Published?:
Published
Last Modified:
29 Sep 2020 04:54