Lagrangian Two-spheres Can Be Symplectically Knotted
نویسنده
چکیده
In the past few years there have been several striking results about the topology of Lagrangian surfaces in symplectic four-manifolds. The general tendency of these results is that many isotopy classes of embedded surfaces do not contain Lagrangian representatives. This is called the topological unknottedness of Lagrangian surfaces; see [4] for a survey. The aim of this paper is to complement this picture by showing that Lagrangian surfaces can be symplectically knotted in infinitely many inequivalent ways. That is to say, a single isotopy class of embedded surfaces can contain infinitely many Lagrangian representatives which are non-isotopic in the Lagrangian sense. The symplectic four-manifolds for which we prove this are non-compact in a mild sense; they are interiors of compact symplectic manifolds with contact type boundary. For instance, one can take
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