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Constructing exact Lagrangian immersions with few double points |
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| Authors: | Tobias Ekholm Yakov Eliashberg Emmy Murphy Ivan Smith |
| Affiliation: | 1. Department of Mathematics, Uppsala University, Box 480, 751 06, Uppsala, Sweden 2. Institute Mittag-Leffler, Aurav?gen 17, 182 60, Djursholm, Sweden 3. Department of Mathematics, Stanford University, Stanford, CA, 94305-2125, USA 4. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA, 02139, USA 5. Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, England |
| 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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