The First Coefficient of the Conway Polynomial
نویسندگان
چکیده
منابع مشابه
The 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...
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15 صفحه اولChirality 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 ...
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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....
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1985
ISSN: 0002-9939
DOI: 10.2307/2044531