Friday May 10th, 2024 | |
| Time: | 2:30 PM - 1:00 AM |
| Title: | GLOBAL SURFACES OF SECTION FOR REEB FLOWS ON CLOSED 3-MANIFOLDS |
| Speaker: | Marco Mazzucchelli, ENS Lyon |
| Abstract: | |
| Global surfaces of section are tools that allow to reduce the study of the dynamics of a nowhere vanishing vector field on a 3-manifold to the study of a surface diffeomorphism. Poincaré introduced global surfaces of sections in his study of the planar circular restricted 3-body problem from celestial mechanics. While certain vector fields (such as the one generating the horocycle flow) do not admit a global surface of section, it is conjectured that all Reeb flows of 3-dimensional closed manifolds do. In this talk, which is based on joint work with Gonzalo Contreras, I will sketch a proof of this conjecture for the Reeb flows of C^∞-generic contact forms on any closed 3-manifold. This generic family includes all contact forms whose Reeb flows are non-degenerate and satisfy the Kupka-Smale transversality condition. | |