Volume 18, issue 2 (2014)

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Unlinking and unknottedness of monotone Lagrangian submanifolds

Georgios Dimitroglou Rizell and Jonathan David Evans

Geometry & Topology 18 (2014) 997–1034
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.

Keywords
Lagrangian submanifold, symplectic manifold, monotone, torus, knot
Primary: 53D12