Exact Lagrangian caps of Legendrian knots

2013/09/19 by Lin, Francesco · 3 citations
#FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1309.5101

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 show this, we construct a family combinatorial moves on knot projections with some additional data that correspond to Lagrangian cobordisms between knots.

Cited by

• Non-decomposable Lagrangian cobordisms between Legendrian knots
• Regular Lagrangians in Lefschetz fibrations
• Non-regular Lagrangian concordances between Lagrangian fillable Legendrian knots

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• Lagrangian Fillings of Legendrian 4-Plat Knots
• An obstruction to decomposable exact Lagrangian fillings
• Constructions of Lagrangian cobordisms
• Legendrian Satellites and Decomposable Concordances