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