GLOBAL SURFACES OF SECTION FOR REEB FLOWS ON CLOSED 3-MANIFOLDS
数学公众报告（120周年校庆系列第9场）
报告题目(Title)：GLOBAL SURFACES OF SECTION FOR REEB FLOWS ON CLOSED 3-MANIFOLDS
报告人(Speaker)：Marco Mazzucchelli 教授 （Ecole Normale Superieure de Lyon）
地点(Place)：Zoom meeting ID: 86953441232, 密码：123456
时间(Time)：2022 年 01 月 21 日（周五） 16:00--17:00
邀请人(Inviter)：苏喜锋
报告摘要
In this talk, which is based on joint work with Gonzalo Contreras, I will sketch a proof of the existence of global surfaces of section for any Reeb vector field of a closed 3-manifold satisfying the Kupka-Smale condition. In particular, this establishes the existence of global surfaces of section for the Reeb vector fields of $C^\infty-generic$ contact forms on a closed 3-manifold, and for the geodesic vector fields of $C^\infty-generic$ Riemannian metrics on closed surfaces. Time permitting, I will also mention other results for geodesic flows of $C^2$-generic Riemannian metrics on closed surfaces, obtained with similar techniques: a dichotomy between the existence of elliptic closed geodesics and the Anosov property, and a proof of the stability conjecture (a $C^2$-structurally stable Riemannian geodesic flow of a closed surface is Anosov).
