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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Licata, J.E. (2011). Legendrian Grid Number One Knots and Augmentations of Their Differential Algebras. In: Banagl, M., Vogel, D. (eds) The Mathematics of Knots. Contributions in Mathematical and Computational Sciences, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15637-3_6
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DOI: https://doi.org/10.1007/978-3-642-15637-3_6
Publisher Name: Springer, Berlin, Heidelberg
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