The Bennequin Number, Kauffman Polynomial, and Ruling Invariants of A Legendrian Link: the Fuchs Conjecture and Beyond
نویسنده
چکیده
We show that the ungraded ruling invariants of a legendrian link can be realized as certain coefficients of the Kauffman polynomial which are non-vanishing if and only if the upper bound for the Bennequin number given by the Kauffman polynomial is sharp. This resolves positively a conjecture of Fuchs. Using similar methods a result involving the upper bound given by the HOMFLY polynomial and 2-graded rulings is proved.
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