Classification results for two-dimensional Lagrangian tori

Vendredi 22 avril 2016 15:30-16:30 - Georgios Dimitroglou Rizell - Cambridge

Résumé : We present several classification results for Lagrangian tori, all proven using the splitting construction from symplectic field theory. Notably, we classify Lagrangian tori in the symplectic vector space up to Hamiltonian isotopy ; they are either product tori or rescalings of the Chekanov torus. The proof uses the following results established in a recent joint work with E. Goodman and A. Ivrii. First, there is a unique torus up to Lagrangian isotopy inside the symplectic vector space, the projective plane, as well as the monotone S2 x S2. Second, the nearby Lagrangian conjecture holds for the cotangent bundle of the torus.

Lieu : 113-115

Classification results for two-dimensional Lagrangian tori  Version PDF