We provide a translation between Chekanov's combinatorial theory for of Legendrian knows in the standard contact ℝ3 Eliashberg and Hofer's contact homology. We use this translation to the idea of "coherent orientations" from the contact homology world to's combinatorial setting. As a result, we obtain a lifting of Chekanov's graded algebra invariant to an algebra over ℤ[t,t-1] with a fullℤ grading.
No takes yet. Share an insight, caveat, or question.
Etnyre et al. (2001) studied this question.