Constructing exact Lagrangian immersions with few double points

Tobias Ekholm, Yakov Eliashberg*, Emmy Murphy, Ivan Smith

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

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 ℝst6 with exactly one transverse double point. Our construction also yields a Lagrangian embedding S1 × S2 → ℝst6 with vanishing Maslov class.

Original languageEnglish (US)
Pages (from-to)1772-1803
Number of pages32
JournalGeometric and Functional Analysis
Volume23
Issue number6
DOIs
StatePublished - Dec 2013

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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