English

Exact Lagrangian immersions with a single double point

Symplectic Geometry 2014-11-25 v2

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.

Keywords

Cite

@article{arxiv.1111.5932,
  title  = {Exact Lagrangian immersions with a single double point},
  author = {Tobias Ekholm and Ivan Smith},
  journal= {arXiv preprint arXiv:1111.5932},
  year   = {2014}
}

Comments

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

R2 v1 2026-06-21T19:41:25.941Z