Lagrangian surfaces in a fixed homology class: existence of knotted Lagrangian tori

Abstract

In this paper we show that there exist simply connected symplectic manifolds which contain infinitely many knotted lagrangian tori, i.e., nonisotopic lagrangian tori that are image of homotopic embeddings. Moreover, the homology class they represent can be assumed to be nontrivial and primitive. This answers a question of Eliashberg and Polterovich.