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 \({\mathbb{R}^6_{\rm st}}\) with exactly one transverse double point. Our construction also yields a Lagrangian embedding \({S^1 \times S^2 \to \mathbb{R}^6_{\rm st}}\) with vanishing Maslov class.
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T. Ekholm is partially supported by Swedish Research Council Grant 2012-2365 and by the Knut and Alice Wallenberg Foundation as a Wallenberg Scholar.
Y. Eliashberg is partially supported by NSF grant DMS-1205349.
E. Murphy is partially supported by NSF grant DMS-0943787.
I. Smith is partially supported by grant ERC-2007-StG-205349 from the European Research Council.
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Ekholm, T., Eliashberg, Y., Murphy, E. et al. Constructing exact Lagrangian immersions with few double points. Geom. Funct. Anal. 23, 1772–1803 (2013). https://doi.org/10.1007/s00039-013-0243-6
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DOI: https://doi.org/10.1007/s00039-013-0243-6