Conway polynomial and oriented rotant links
This paper gives a positive answer to the question, raised in [\textit{G. T. Jin} and \textit{D. Rolfsen}, Can. Math. Bull., 34, 480--484 (1991; Zbl 0754.57002)], of whether the Conway polynomials agree for oriented \(n\)-rotants of all orders \(n\). A pair of links \(L_1\) and \(L_2\) are called oriented rotants of order \(n\) if \(L_2\) has a diagram obtained from that of \(L_1\) in the following way: let \(R_1\) be the part of the diagram of \(L_1\) contained in a disk \(B\) and invariant under a rotation by angle \(2\pi/n\); the diagram of \(L_2\) is obtained by rotating \(R_1\) by \(\pi\) through the space around an axis lying on the plane of the diagram and reversing all orientations of the strings on \(R_1\). The author proves that the Conway polynomials of a pair of oriented rotants of any order coincide. The idea of the proof is to translate the topological problem into one of linear algebra. More precisely, the equality of the Conway polynomials follows from the equality of the determinants of certain Hermitian matrices associated with the Conway potential.
scientific article; zbMATH DE number 2165502
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