Putting Contact Geometry in Order: Orderability and Contact Rigidity

Using loops of contactomorphisms generated by vector fields that are positively transverse to the contact distribution, Eliashberg and Polterovich introduced the notion of orderability for contact manifolds. Recent work seems to suggest that the resulting dichotomy marks a boundary between more flexible contact manifolds and contact manifolds that show some signs of rigidity. 

In this talk, I will introduce orderability and illustrate it through various examples of orderable and non-orderable contact manifolds. 

We will further explore examples for the connection between orderability and contact rigidity through results on translated points, unbounded conjugation-invariant norms, contact non-squeezing, and the non-displaceability of pre-Lagrangian submanifolds.