Constructing exact Lagrangian immersions with few double points
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Murphy_Constructing exact.pdf
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Author(s)
Ekholm, Tobias
Eliashberg, Yakov
Murphy, Emmy
Smith, Ivan
Date Issued
August 2013
Journal
Geometric and Functional Analysis
Publisher
Springer-Verlag
Citation
Ekholm, Tobias, Yakov Eliashberg, Emmy Murphy, and Ivan Smith. “Constructing Exact Lagrangian Immersions with Few Double Points.” Geometric and Functional Analysis 23, no. 6 (December 2013): 1772–1803.
Version
Original manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00039-013-0243-6
