Lagrangian unknottedness in Stein surfaces

We show that the space of Lagrangian spheres inside the cotangent bundle of the 2-sphere is contractible. We then discuss the phenomenon of Lagrangian unknottedness in other Stein surfaces. There exist homotopic Lagrangian spheres which are not Hamiltonian isotopic, but we show that in a typical case all such spheres are still equivalent under a symplectomorphism.

Keywords

Stein manifolds, Lagrangian submanifolds, Hamiltonian diffeomorphisms, symplectic Dehn twists

2010 Mathematics Subject Classification

32Q65, 53D12

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Published 8 March 2012