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

Nikolas Adaloglou; Jonathan David Evans

doi:10.4171/cmh/620

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

Nikolas Adaloglou
Sorbonne University, Paris, France
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Jonathan David Evans
Lancaster University, UK

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

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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 $Z_{2}$ -homology class of an $S^{2}$ -factor if the symplectic area of that factor is at least twice that of the other.

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Nikolas Adaloglou, Jonathan David Evans, Lagrangian Klein bottles in $S^{2} \times S^{2}$ . Comment. Math. Helv. (2026), published online first

DOI 10.4171/CMH/620