Exact Lagrangian caps of Legendrian knots

Francesco Lin

doi:10.4310/JSG.2016.v14.n1.a10

Exact Lagrangian caps of Legendrian knots

Francesco Lin

Mathematics

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

9 Scopus citations

Abstract

We prove that any Legendrian knot in (S³, ξ_std) bounds an exact Lagrangian surface in ℝ⁴ \ B⁴ after a sufficient number of stabilizations. In order to do this, we define Lagrangian projections, consisting of a knot projection along with some additional information, and construct a family of combinatorial moves which correspond to Lagrangian cobordisms between knots.

Original language	English (US)
Pages (from-to)	269-295
Number of pages	27
Journal	Journal of Symplectic Geometry
Volume	14
Issue number	1
DOIs	https://doi.org/10.4310/JSG.2016.v14.n1.a10
State	Published - 2016

All Science Journal Classification (ASJC) codes

Geometry and Topology

Access to Document

10.4310/JSG.2016.v14.n1.a10

Cite this

@article{3d9c1f9d51dc439fb348326254bd58f7,

title = "Exact Lagrangian caps of Legendrian knots",

abstract = "We prove that any Legendrian knot in (S3, ξstd) bounds an exact Lagrangian surface in ℝ4 \textbackslash{} B4 after a sufficient number of stabilizations. In order to do this, we define Lagrangian projections, consisting of a knot projection along with some additional information, and construct a family of combinatorial moves which correspond to Lagrangian cobordisms between knots.",

author = "Francesco Lin",

year = "2016",

doi = "10.4310/JSG.2016.v14.n1.a10",

language = "English (US)",

volume = "14",

pages = "269--295",

journal = "Journal of Symplectic Geometry",

issn = "1527-5256",

publisher = "International Press of Boston, Inc.",

number = "1",

}

TY - JOUR

T1 - Exact Lagrangian caps of Legendrian knots

AU - Lin, Francesco

PY - 2016

Y1 - 2016

N2 - We prove that any Legendrian knot in (S3, ξstd) bounds an exact Lagrangian surface in ℝ4 \ B4 after a sufficient number of stabilizations. In order to do this, we define Lagrangian projections, consisting of a knot projection along with some additional information, and construct a family of combinatorial moves which correspond to Lagrangian cobordisms between knots.

AB - We prove that any Legendrian knot in (S3, ξstd) bounds an exact Lagrangian surface in ℝ4 \ B4 after a sufficient number of stabilizations. In order to do this, we define Lagrangian projections, consisting of a knot projection along with some additional information, and construct a family of combinatorial moves which correspond to Lagrangian cobordisms between knots.

UR - https://www.scopus.com/pages/publications/84976303007

UR - https://www.scopus.com/inward/citedby.url?scp=84976303007&partnerID=8YFLogxK

U2 - 10.4310/JSG.2016.v14.n1.a10

DO - 10.4310/JSG.2016.v14.n1.a10

M3 - Article

AN - SCOPUS:84976303007

SN - 1527-5256

VL - 14

SP - 269

EP - 295

JO - Journal of Symplectic Geometry

JF - Journal of Symplectic Geometry

IS - 1

ER -

Exact Lagrangian caps of Legendrian knots

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this