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Unlinking and
unknottedness of monotone Lagrangian submanifolds
Georgios Dimitroglou Rizell and Jonathan David Evans |
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Geometry & Topology 18 (2014) 997–1034
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Abstract |
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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. |
Keywords
Lagrangian submanifold, symplectic manifold, monotone,
torus, knot
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Mathematical Subject Classification 2010
Primary: 53D12
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References |
Publication
Received: 29 November 2012
Revised: 16 September 2013
Accepted: 16 October 2013
Published: 7 April 2014
Proposed: Leonid Polterovich
Seconded: Yasha Eliashberg, Simon Donaldson
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Authors |
| Georgios Dimitroglou Rizell | |
| Laboratoire de Mathématiques
d’Orsay Université Paris-Sud Bâtiment 425 F-91405 Orsay France |
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| Jonathan David Evans | |
| Department of Mathematics University College London Gower Street London WC1E 6BT UK |
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