Legendrian grid number one knots and augmentations of their differential algebras
Geometric Topology
2010-03-22 v1 Symplectic Geometry
Abstract
In this article we study the differential graded algebra (DGA) invariant associated to Legendrian knots in tight lens spaces. Given a grid number one diagram for a knot in L(p, q), we show how to construct a special Lagrangian diagram suitable for computing the DGA invariant for the Legendrian knot specified by the diagram. We then specialize to L(p, p - 1) and show that for two families of knots, the existence of an augmentation of the DGA depends solely on the value of p.
Cite
@article{arxiv.1003.3685,
title = {Legendrian grid number one knots and augmentations of their differential algebras},
author = {Joan E. Licata},
journal= {arXiv preprint arXiv:1003.3685},
year = {2010}
}
Comments
21 pages, 13 figures, to appear in the Proceedings of the Heidelberg Knot Theory Semester