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

2001/06/15 by Klaus Mohnke, Mohnke, Klaus · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.SG

paper · pdf · doi:10.48550/arxiv.math/0106139

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

openalex publication_date 2001/06/15 · arxiv created 2003/07/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that there exists no Lagrangian embeddings of the Klein bottle into \CC². Using the same techniques we also give a new proof that any Lagrangian torus in \CC² is smoothly isotopic to the Clifford torus.

Cited by

• Lagrangian embeddings of the Klein bottle and combinatorial properties of mapping class groups
• Monodromy groups of Lagrangian tori in the symplectic 4-space

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