Exact Lagrangian immersions with a single double point

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.

51 pages, 1 figure. Version 2: minor changes to incorporate referees' suggestions. This version to appear in JAMS

References in corpus (1)

• Floer homology on the universal cover, a proof of Audin's conjecture and other constraints on Lagrangian submanifolds

Cited by in corpus (3)

• On the immersion classes of nearby Lagrangians
• Constructing exact Lagrangian immersions with few double points
• A symplectic prolegomenon