Constructing exact Lagrangian immersions with few double points

Abstract

We establish, as an application of the results from Eliashberg and Murphy (Lagrangian caps, 2013), 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 over st] with exactly one transverse double point. Our construction also yields a Lagrangian embedding S[superscript 1] × S[superscript 2] → R[6 over st] with vanishing Maslov class.