Constructing exact Lagrangian immersions with few double points

Tobias Ekholm; Yakov Eliashberg; Emmy Murphy; Ivan Smith

doi:10.1007/s00039-013-0243-6

Constructing exact Lagrangian immersions with few double points

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

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

24 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 ℝ_st⁶ with exactly one transverse double point. Our construction also yields a Lagrangian embedding S¹ × S² → ℝ_st⁶ with vanishing Maslov class.

Original language	English (US)
Pages (from-to)	1772-1803
Number of pages	32
Journal	Geometric and Functional Analysis
Volume	23
Issue number	6
DOIs	https://doi.org/10.1007/s00039-013-0243-6
State	Published - Dec 2013

Funding

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.

ASJC Scopus subject areas

Analysis
Geometry and Topology

Access to Document

10.1007/s00039-013-0243-6

Cite this

@article{929bbb264ca749239cb59ab5f5356c72,

title = "Constructing exact Lagrangian immersions with few double points",

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.",

author = "Tobias Ekholm and Yakov Eliashberg and Emmy Murphy and Ivan Smith",

note = "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.",

year = "2013",

month = dec,

doi = "10.1007/s00039-013-0243-6",

language = "English (US)",

volume = "23",

pages = "1772--1803",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Birkhauser Verlag Basel",

number = "6",

}

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.

UR - http://www.scopus.com/inward/record.url?scp=84888439512&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888439512&partnerID=8YFLogxK

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 -

Constructing exact Lagrangian immersions with few double points

Abstract

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this