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

7 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 - Jan 1 2016

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.4310/JSG.2016.v14.n1.a10

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abstract = "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.",

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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.

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Exact Lagrangian caps of Legendrian knots

Abstract

All Science Journal Classification (ASJC) codes

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