Exact Lagrangian caps of Legendrian knots
Francesco Lin

TL;DR
This paper proves that after enough stabilizations, any Legendrian knot in the standard 3-sphere bounds an exact Lagrangian surface in four-dimensional space, using combinatorial moves on knot projections.
Contribution
It introduces a new combinatorial framework of moves on knot projections that correspond to Lagrangian cobordisms, enabling the construction of exact Lagrangian caps.
Findings
Any Legendrian knot can be capped with an exact Lagrangian surface after stabilizations.
Develops a set of combinatorial moves representing Lagrangian cobordisms.
Provides a method to construct Lagrangian caps for Legendrian knots.
Abstract
We prove that any Legendrian knot in bounds an exact Lagrangian surface in 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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Connective tissue disorders research
