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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