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arXiv · 1003.3685

Legendrian grid number one knots and augmentations of their differential algebras

Joan E. Licata
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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.

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Joan E. Licata. 2010-03-18. Legendrian grid number one knots and augmentations of their differential algebras. https://arxiv.org/abs/1003.3685

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