GT seminar: Arnol'd's chord conjecture for conormal Legendrian lifts
- Date
- 22 January 2026, 14:15–15:15
- Location
- Ångström Laboratory, 64119
- Type
- Seminar
- Lecturer
- Filip Broćić (University of Augsburg)
- Organiser
- Matematiska Institutionen
- Contact person
- Alex Takeda
Filip Broćić (University of Augsburg) will give this seminar talk. All are welcome to join!
Abstract: The chord conjecture, due initially to Arnol'd in the case of the standard contact three-sphere, asserts the existence of a Reeb chord with boundary on every closed Legendrian submanifold of a closed contact manifold for every contact form. This conjecture was established in various settings by Cieliebak, Mohnke, Hutchings and Taubes, and others. In this talk, I will sketch a proof of the chord conjecture for conormal bundles of closed submanifolds of any closed manifold seen as Legendrians in the co-sphere bundle. This generalizes a result of Grove in Riemannian geometry regarding the existence of geodesics normal to the submanifold. The method of proof involves wrapped Floer cohomology with local coefficients. This talk is based on joint work with Dylan Cant and Egor Shelukhin.
This is a talk in our Geometry and Topology Seminar Series.