Exact Lagrangian immersions with a single double point

2011/11/25 by Tobias Ekholm, Ivan Smith, Ekholm, Tobias +1 · 1 citation
Mathematics · #53D35 #53D40 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1111.5932

openalex publication_date 2011/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k > 2. We show that if a closed orientable 2k-manifold K, with Euler characteristic not equal to -2, admits an exact Lagrangian immersion into complex Euclidean 2k-space with one transverse double point and no other self-intersections, then K is diffeomorphic to the standard sphere. The proof combines Floer homological arguments with a detailed study of moduli spaces of holomorphic disks with boundary in a monotone Lagrangian submanifold obtained by Lagrange surgery on K.

Citations

• Quantum K -theory, I: Foundations
• Floer homology on the universal cover, a proof of Audin's conjecture and other constraints on Lagrangian submanifolds
• Effect of Legendrian Surgery

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• Normal invariant of nearby Lagrangians via twisted derivative

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