Non-Orientable Lagrangian Fillings of Legendrian Knots
Non-Orientable Lagrangian Fillings of Legendrian Knots
Abstract We investigate when a Legendrian knot in the standard contact ${{\mathbb{R}}}^3$ has a non-orientable exact Lagrangian filling. We prove analogs of several results in the orientable setting, develop new combinatorial obstructions to fillability, and determine when several families of knots have such fillings. In particular, we completely determine when …