• Corpus ID: 15621252

How to (symplectically) thread the eye of a (Lagrangian) needle

@article{Mohnke2001HowT,
  title={How to (symplectically) thread the eye of a (Lagrangian) needle},
  author={Klaus Mohnke},
  journal={arXiv: Symplectic Geometry},
  year={2001}
}
  • K. Mohnke
  • Published 15 June 2001
  • Mathematics
  • arXiv: Symplectic Geometry
We show that there exists no Lagrangian embeddings of the Klein bottle into $\CC^{2}$. Using the same techniques we also give a new proof that any Lagrangian torus in $\CC^2$ is smoothly isotopic to the Clifford torus. 
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Lefschetz pencils, Morse functions, and Lagrangian embeddings of the Klein bottle
It is shown that the mod 2 homology class represented by a Lagrangian Klein bottle in a complex algebraic surface is non-zero. In particular, the Klein bottle does not admit a Lagrangian embedding
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