Non-Orientable Lagrangian Fillings of Legendrian Knots

Geometry Topology Seminar
Monday, February 12, 2018 - 14:00
1 hour (actually 50 minutes)
Skiles 006
Haverford College
Lagrangian fillings of Legendrian knots are interesting objects that are related, on one hand, to the 4-genus of the underlying smooth knot and, on the other hand, to Floer-type invariants of Legendrian knots. Most work on Lagrangian fillings to date has concentrated on orientable fillings.  I will present some first steps in constructions of and obstructions to the existence of (decomposable exact) non-orientable Lagrangian fillings.  In addition, I will discuss links between the 4-dimensional crosscap number of a knot and the non-orientable Lagrangian fillings of its Legendrian representatives. This is joint work in progress with Linyi Chen, Grant Crider-Philips, Braeden Reinoso, and Natalie Yao.