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.Comment: v2: 10 pages, 3 figures; minor revisions, to appear in Pacific J.
  Mat

Joshua

Lenhard L. Ng

M. Sabloff

English

arXiv

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

Lenhard, L. Ng

Sabloff, Joshua Marc

Haverford College: Haverford Scholarship

The Correspondence Between Augmentations and Rulings for Legendrian Knots

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.233.8733

The correspondence between augmentations and rulings for Legendrian knots

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Haverford College: Haverford Scholarship