Vol. 258, No. 2, 2012

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Generalized normal rulings and invariants of Legendrian solid torus links

Mikhail Lavrov and Dan Rutherford

Vol. 258 (2012), No. 2, 393–420

For Legendrian links in the 1-jet space of S1 we show that the 1-graded ruling polynomial may be recovered from the Kauffman skein module. For such links a generalization of the notion of normal ruling is introduced. We show that the existence of such a generalized normal ruling is equivalent to sharpness of the Kauffman polynomial estimate for the Thurston–Bennequin number as well as to the existence of an ungraded augmentation of the Chekanov–Eliashberg DGA. Parallel results involving the HOMFLY-PT polynomial and 2-graded generalized normal rulings are established.

Legendrian knot, Kauffman polynomial, skein module, normal ruling
Mathematical Subject Classification 2010
Primary: 57M27, 57R17
Received: 4 October 2011
Revised: 8 December 2011
Accepted: 18 December 2011
Published: 1 August 2012
Mikhail Lavrov
Carnegie Mellon University
Pittsburgh, PA 15213
United States
Dan Rutherford
University of Arkansas
Fayetteville, AR 72701
United States