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Lagrangian two-spheres can be symplectically knotted

Paul Seidel
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Abstract

This paper shows that there are symplectic four-manifolds M with the following property: a single isotopy class of smooth embedded two-spheres in M contains infinitely many Lagrangian submanifolds, no two of which are isotopic as Lagrangian submanifolds. The examples are constructed using a special class of symplectic automorphisms ("generalized Dehn twists"). The proof uses Floer homology. Revised version: one footnote removed, one reference added

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Paul Seidel. 2000-05-31. Lagrangian two-spheres can be symplectically knotted. https://arxiv.org/abs/math/9803083

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