The correspondence between augmentations and rulings for Legendrian knots

Lenhard L. Ng and Joshua M. Sabloff

Vol. 224 (2006), No. 1, 141–150

DOI: 10.2140/pjm.2006.224.141

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.

Keywords

Legendrian knots, generating functions, contact homology, augmentations

Mathematical Subject Classification 2000

Primary: 57R17

Secondary: 53D40, 57M25

Milestones

Received: 9 March 2005

Revised: 29 July 2005

Accepted: 26 August 2005

Published: 1 March 2006