On Alexander–Conway polynomials of two-bridge links
نویسندگان
چکیده
منابع مشابه
On Alexander-Conway polynomials of two-bridge links
We consider Conway polynomials of two-bridge links as Euler continuant polynomials. As a consequence, we obtain simple proofs of the classical theorems of Murasugi and Hartley on Alexander polynomials. We give a modulo 2 congruence for links, which implies the classical modulo 2 Murasugi congruence for knots. We also give sharp bounds for the coefficients of the Conway and Alexander polynomials...
متن کاملThe Skein Module of Two-bridge Links
We calculate the Kauffman bracket skein module (KBSM) of the complement of all two-bridge links. For a two-bridge link, we show that the KBSM of its complement is free over the ring C[t] and when reducing t = −1, it is isomorphic to the ring of regular functions on the character variety of the link group.
متن کاملLegendrian Framings for Two-bridge Links
We define the Thurston-Bennequin polytope of a twocomponent link as the convex hull of all pairs of integers that arise as framings of a Legendrian representative. The main result of this paper is a description of the Thurston-Bennequin polytope for two-bridge links. As an application, we construct non-quasipositive surfaces in R all whose sub-annuli are quasipositive.
متن کاملA-polynomials of a Family of Two-bridge Knots
The J(k, l) knots, often called the double twist knots, are a subclass of two-bridge knots which contains the twist knots. We show that the A-polynomial of these knots can be determined by an explicit resultant. We present this resultant in two different ways. We determine a recursive definition for the A-polynomials of the J(4, 2n) and J(5, 2n) knots, and for the canonical component of the A-p...
متن کاملMaximal Thurston-bennequin Number of Two-bridge Links
We compute the maximal Thurston-Bennequin number for a Legendrian two-bridge knot or oriented two-bridge link in standard contact R, by showing that the upper bound given by the Kauffman polynomial is sharp. As an application, we present a table of maximal Thurston-Bennequin numbers for prime knots with nine or fewer crossings.
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2015
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2014.09.011