Non-Orientable Lagrangian Fillings of Legendrian Knots

Most work on Lagrangian fillings of Legendrian knots to date has concentrated on orientable fillings, but instead I will present some first steps in constructions of and (especially) obstructions to the existence of (decomposable exact) non-orientable Lagrangian fillings.

This is joint work in progress with Linyi Chen, Grant Crider-Philips, Braeden Reinoso, and Natalie Yao.