Exact Lagrangian caps of Legendrian knots

Francesco Lin

Exact Lagrangian caps of Legendrian knots

Symplectic Geometry 2013-09-23 v1 Geometric Topology

Authors: Francesco Lin

Abstract

We prove that any Legendrian knot in $(S^3,\xi_{std})$ bounds an exact Lagrangian surface in $\mathbb{R}^4\setminus B^4$ 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.

Keywords

Legendrian knots exact Lagrangian caps stabilizations Lagrangian cobordisms knot projections combinatorial moves symplectic geometry

Cite

@article{arxiv.1309.5101,
  title  = {Exact Lagrangian caps of Legendrian knots},
  author = {Francesco Lin},
  journal= {arXiv preprint arXiv:1309.5101},
  year   = {2013}
}

Comments

22 pages, 25 figures

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