Generalized normal rulings and invariants of Legendrian solid torus links

Details Generalized normal rulings and invariants of Legendrian solid torus links Generalized normal rulings and invariants of Legendrian solid torus links

2011-09-06

arxiv.org/abs/1109.1319v1

Mathematics

Geometric Topology

26 pages, 6 figures

Scientific paper

For Legendrian links in the 1-jet space of $S^1$ 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.

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