Positive loops and orderability in contact geometry

Princeton/IAS Symplectic Geometry Seminar
Topic:Positive loops and orderability in contact geometry
Speaker:Peter Weigel
Affiliation:Purdue University
Date:Friday, October 4
Time/Room:1:00pm - 2:00pm/S-101
Video Link:https://video.ias.edu/pisgs/2013/1004-PeterWeigel

Orderability of contact manifolds is related in some non-obvious ways to the topology of a contact manifold \(\Sigma\). We know, for instance, that if \(\Sigma\) admits a 2-subcritical Stein filling, it must be non-orderable. By way of contrast, in this talk I will discuss ways of modifying Liouville structures for high-dimensional \(\Sigma\) so that the result is always orderable. The main technical tool is a Morse-Bott Floer theoretic growth rate, which has some parallels with Givental's nonlinear Maslov index. I will also discuss a generalization to the relative case, and applications to bi-invariant metrics on \(\mathrm{Cont}(\Sigma)\).