Attention : séance exceptionnelle un lundi
Let X be a symplectic manifold, and let L be a Lagrangian in X. If a Hamiltonian diffeomorphism preserves L as a subset, what can be said about the induced map on the homology of L? In some cases, one can easily find a non-trivial automorphism on the homology of L. In other cases, the only possible map is the identity. There are works by M. L. Yau, S. Hu - F. Lalonde - R. Leclerq. I will discuss the case of "standard" product tori in a polydisc (the conclusion depends on the size) and the product of equators in a product of two-spheres.