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 $\mathrm{Cont}(\Sigma)$.