Joint IAS/Princeton University Symplectic Geometry Seminar

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