Invariants of Legendrian knots and coherent orientations
Joint work with Lenhard Ng and Joshua Sabloff,
J. Sympl. Geom. 1 (2002), no. 2, 321-368.

We provide a translation between Chekanov's combinatorial theory for invariants of Legendrian knots in the standard contact $\R^3$ and a relative version of Eliashberg and Hofer's Contact Homology. We use this translation to transport the idea of ``coherent orientations'' from the Contact Homology world to Chekanov's combinatorial setting. As a result, we obtain a lifting of Chekanov's differential graded algebra invariant to an algebra over $\Z[t, t-1]$ with a full $\Z$ grading.

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