## Lagrangian surfaces in a fixed homology class: existence of knotted Lagrangian tori.(English)Zbl 1105.53061

Summary: We show that there exist simply connected symplectic manifolds which contain infinitely many knotted Lagrangian tori, i.e., nonisotopic Lagrangian tori that are images 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.

### MSC:

 53D12 Lagrangian submanifolds; Maslov index 53D35 Global theory of symplectic and contact manifolds

### Keywords:

symplectically isotopic; homotopy; isotopy
Full Text: