Positive loops and orderability in contact geometry

Positive loops and orderability in contact geometry

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Peter Weigel , Purdue University
IAS - Simonyi Hall Seminar Room SH-101

PLEASE NOTE DIFFERENT TIME.  Orderability of contact manifolds is related in some non-obvious ways to the topology of a contact manifold Σ. We know, for instance, that if Σ 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 Σ 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 Cont(Σ).