Invariants of Legendrian Knots and Coherent Orientations

Details Invariants of Legendrian Knots and Coherent Orientations Invariants of Legendrian Knots and Coherent Orientations

2001-01-17

arxiv.org/abs/math/0101145v3

J. Symplectic Geom. 1 (2002), 321-367

Mathematics

Symplectic Geometry

32 pages, 17 figures; small technical corrections to proof of Thm 3.7 and example 4.3

Scientific paper

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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