TY - JOUR
T1 - Constructing exact Lagrangian immersions with few double points
AU - Ekholm, Tobias
AU - Eliashberg, Yakov
AU - Murphy, Emmy
AU - Smith, Ivan
N1 - Funding Information:
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.
PY - 2013/12
Y1 - 2013/12
N2 - 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.
AB - 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.
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U2 - 10.1007/s00039-013-0243-6
DO - 10.1007/s00039-013-0243-6
M3 - Article
AN - SCOPUS:84888439512
SN - 1016-443X
VL - 23
SP - 1772
EP - 1803
JO - Geometric and Functional Analysis
JF - Geometric and Functional Analysis
IS - 6
ER -