M Sabloff, Invariants of Legendrian knots and coherent orientations

Abstract. We provide a translation between Chekanov’s combinatorial theory for invari-ants of Legendrian knots in the standard contact R3 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. 1