Lagrangian Klein bottles in $S^2\times S^2$

Abstract

We use Luttinger surgery to show that there are no Lagrangian Klein bottles in $S^2\times S^2$ in the ${\mathbb{Z}}_2$-homology class of an $S^2$-factor if the symplectic area of that factor is at least twice that of the other.

13 pages, 4 figures