A Lagrangian Klein bottle you can't squeeze

TL;DR

This paper investigates the deformation limits of a specific nonorientable Lagrangian Klein bottle within a symplectic 4-manifold, addressing how much the symplectic form can be altered before losing the Lagrangian property.

Contribution

It provides a solution to the deformation question for a particular Lagrangian Klein bottle and discusses related conjectures in symplectic topology.

Findings

Determined the deformation limits for the Lagrangian Klein bottle

Identified conditions under which the Klein bottle ceases to be Lagrangian

Discussed implications for related symplectic topology conjectures

Abstract

Suppose you have a nonorientable Lagrangian surface L in a symplectic 4-manifold. How far can you deform the symplectic form before the smooth isotopy class of L contains no Lagrangians? I solve this question for a particular Lagrangian Klein bottle. I also discuss some related conjectures.