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

Adaloglou, Nikolas and Evans, Jonny (2026) Lagrangian Klein bottles in $S^{2}\times S^{2}$. Commentarii Mathematici Helvetici. ISSN 0010-2571

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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.