Lagrangian Surfaces in a Fixed Homology Class: Existence of Knotted Lagrangian Tori
Abstract
In this paper we show that there exist simply connected symplectic 4-manifolds which contain infinitely many knotted lagrangian tori, i.e. lagrangian embeddings of tori that are homotopic but not isotopic. Moreover, the homology class they represent can be assumed to be nontrivial and primitive. This answers a question of Eliashberg and Polterovich.
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