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

Abstract

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.

revised version, 15 pages, no figures, easier proof, clearer structured