Research ArticleNo Access

On two-bridge knots and a conjecture of Hirasawa–Murasugi

Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany

https://doi.org/10.1142/S0218216521500073Cited by:3 (Source: Crossref)

Abstract

Fox conjectured the Alexander polynomial of an alternating knot is trapezoidal, i.e. the absolute values of the coefficients first increase, then stabilize and finally decrease in a symmetric way. Recently, Hirasawa and Murasugi further conjectured a relation between the number of the stable coefficients in the Alexander polynomial and the signature invariant. In this paper we prove the Hirasawa–Murasugi conjecture for two-bridge knots.

Keywords:

AMSC: 57K10, 57K14

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