The Correspondence Between Augmentations and Rulings for Legendrian Knots

This paper investigates connections between two different invariants for Legendrian knots. Though the geometry behind the two invariants, called rulings and augmentations, differs greatly, they are tantalizingly similar to compute in practice. In fact, as this paper shows, there is a connection between the two: namely that one can find the augmentation invariant (an integer) of a Legendrian knot using its ruling invariant (a polynomial). This result provides a starting point for further investigations into connections between the two larger geometric ideas behind the invariants. --author-supplied descriptio