| Résume | Exact Lagrangian submanifolds and Hamiltonian diffeomorphisms play a central role in symplectic topology, particularly in problems related to Arnold’s conjecture on fixed points and Lagrangian intersections. Using Floer theory, one can associate spectral invariants to these objects that lead to a metric on the sets of exact Lagrangian submanifolds and Hamiltonian diffeomorphisms and also to the question of understanding the limit under this metric. This motivates the study of completion of these sets that were firstly studied by Vincent Humilière, as well as the notion of γ-support associated to elements of these completions that has recently been developed by Claude Viterbo. In this talk, after reviewing some preliminaries in symplectic topology, I will introduce the notion of γ-support, describe some of its properties, and discuss its applications. If time permits, I will also briefly discuss my ongoing thesis work on a notion of density for the γ-support and its relation to the regularity of the γ-support in a neighborhood of a point.
[V22] Claude Viterbo, On the Supports in the Humilière Completion and γ - Coisotropic Sets. To appear in Journal de l'École polytechnique
[AHV24] Marie-Claude Arnaud, Vincent Humilière, and Claude Viterbo, Higher Dimensional Birkhoff Attractors. To appear in Journal de L'École Polytechnique
[H08] Vincent Humilière, On Some Completions of the Space of Hamiltonian Maps. Bulletin de la Soc. Math. de France 136.3, PP. 373–404 (2008). |
