The correspondence between augmentations and rulings for Legendrian knots
arXiv:math/0503168
Abstract
We strengthen the link between holomorphic and generating-function invariants of Legendrian knots by establishing a formula relating the number of augmentations of a knot's contact homology to the complete ruling invariant of Chekanov and Pushkar.
v2: 10 pages, 3 figures; minor revisions, to appear in Pacific J. Math