Constructing exact Lagrangian immersions with few double points

Abstract

We establish an $h$-principle for exact Lagrangian immersions with transverse self-intersections and the minimal, or near-minimal number of double points. One corollary of our result is that any orientable closed 3-manifold admits an exact Lagrangian immersion into standard symplectic 6-space $\R^6_\st$ with exactly one transverse double point. Our construction also yields a Lagrangian embedding $S^1\times S^2\to\R^6_\st$ with vanishing Maslov class.

In the new version corrected some misprints, added clarifications and filled a small gap in the proof of Lemma 3.4

References in corpus (3)

• Loose Legendrian embeddings in high dimensional contact manifolds
• Exact Lagrangian immersions with a single double point
• Exact Lagrangian immersions with one double point revisited

Cited by in corpus (1)

• Exact Lagrangian immersions with one double point revisited