Legendrian non-isotopic unit conormal bundles in high dimensions

Abstract: For any compact submanifold of $\mathbb{R}^n$, its unit conormal bundle is a compact Legendrian submanifold of the unit cotangent bundle of $\mathbb{R}^n$. In this talk, I will give examples of pairs of compact connected submanifolds of $\mathbb{R}^n$ of codimension greater than 3 such that their unit conormal bundles are not Legendrian isotopic, although these two Legendrian submanifolds cannot be distinguished by classical invariants. The main tools to distinguish them are the strip Legendrian contact homology and a coproduct on it. I will explain that, in a special case including the main examples, the coproduct can be computed by using the idea of string topology.

mathematical physicsalgebraic topologydifferential geometryrepresentation theorystatistics theory

Audience: researchers in the topic

( slides | video )

Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics

Series comments: Virtual coffee starts on Zoom already 15 minutes before the seminar.