Invariants of Legendrian Knots and Coherent Orientations

Abstract

We provide a translation between Chekanov's combinatorial theory for invariants of Legendrian knows in the standard contact ℝ³ and 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.