منابع مشابه
Chirality and the Conway Polynomial
We conjecture that for the Conway polynomial C(z) of an amphicheiral knot, the product C(z)C(iz)C(z 2) must be a square inside the ring of polynomials with Z 4 coefficients. This conjecture has two ancestors. One is a theorem of Kawauchi and Hartley, which says that the Conway polynomial of a strongly amphicheiral knot must decompose as φ(z)φ(−z). This implies our main conjecture, at least for ...
متن کاملChirality and the Conway polynomial
In recent workwith J.Mostovoy and T. Stanford, the author found that for every natural number n, a certain polynomial in the coefficients of the Conway polynomial is a primitive integer-valued degree n Vassiliev invariant, but that modulo 2, it becomes degree n-1. The conjecture then naturally suggests itself that these primitive invariants are congruent to integer-valued degree n-1 invariants....
متن کاملThe First Coefficient of the Conway Polynomial
A formula is given for the first coefficient of the Conway polynomial of a link in terms of its linking numbers. A graphical interpretation of this formula is also given. Introduction. Suppose that L is an oriented link of n components in 53. Associated to L is its Conway polynomial V¿(z), which must be of the form VL(z) = z-1[a0 + alz2+ ■■■+amz2m\. Let VL(z) = VL(z)/z"~1. In this paper we shal...
متن کاملA Factorization of the Conway Polynomial
It is tempting to conjecture that there is some interesting relationship between the Conway polynomial ∇L(z) of a link L and ∇K(z), where K is a knot obtained by banding together the components of L. Obviously they cannot be equal since only terms of even or odd degree appear in ∇L(z), according to whether L has an odd or even number of components. Moreover there are many ways of choosing bands...
متن کاملInfinitely many two-variable generalisations of the Alexander-Conway polynomial
We show that the Alexander-Conway polynomial ∆ is obtainable via a particular one-variable reduction of each two-variable Links– Gould invariant LG , where m is a positive integer. Thus there exist infinitely many two-variable generalisations of ∆. This result is not obvious since in the reduction, the representation of the braid group generator used to define LG does not satisfy a second-order...
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ژورنال
عنوان ژورنال: Topology
سال: 1981
ISSN: 0040-9383
DOI: 10.1016/0040-9383(81)90017-3