The Conway polynomial and amphicheiral knots
نویسندگان
چکیده
منابع مشابه
Infinite Order Amphicheiral Knots
In 1977 Gordon [G] asked whether every class of order two in the classical knot concordance group can be represented by an amphicheiral knot. The question remains open although counterexamples in higher dimensions are now known to exist [CM]. This problem is more naturally stated in terms of negative amphicheiral knots, since such knots represent 2–torsion in concordance; that is, if K is negat...
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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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We give a brief historical overview of the Tait conjectures, made 120 years ago in the course of his pioneering work in tabulating the simplest knots, and solved a century later using the Jones polynomial. We announce the solution, again based on a substantial study of the Jones polynomial, of one (possibly his last remaining?) problem of Tait, with the construction of amphicheiral knots of alm...
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We prove that certain fibered, −amphicheiral knots are rationally slice. Moreover, we show that the concordance invariants ν and Υ(t) from Heegaard Floer homology vanish for a class of knots that includes rationally slice knots.
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2017
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216517500274