A Lagrangian Klein bottle you can’t squeeze

Journal of Fixed Point Theory and Applications（2022）

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摘要

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.

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关键词

Lagrangian submanifold, symplectic geometry, Klein bottle, genus, pseudoholomorphic curve, 53D12, 53D35, 53D42

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