Geodesic
Lefschetz pencils, Morse functions, and Lagrangian embeddings of the Klein bottle
Izvestiya. Mathematics , Tome 66 (2002) no. 1, pp. 151-164

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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 into the standard symplectic four-space. 
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     author = {S. Yu. Nemirovski},
     title = {Lefschetz pencils, {Morse} functions, and {Lagrangian} embeddings of the {Klein} bottle},
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S. Yu. Nemirovski. Lefschetz pencils, Morse functions, and Lagrangian embeddings of the Klein bottle. Izvestiya. Mathematics , Tome 66 (2002) no. 1, pp. 151-164. http://geodesic.mathdoc.fr/item/IM2_2002_66_1_a6/