On two-bridged knot polynomials

Abstract

AbstractThe extended diagram of a two-bridged knot is introduced, and it is shown how the coefficients of the Alexander polynomial of the knot may be read straight from this diagram. Using this result, it is shown by diagram manipulation that a conjecture of Fox about the coefficients of the Alexander polynomial of an alternating knot is true at least for two-bridged knots (which are all alternating).1980 Mathematics subject classification (Amer. Math. Soc.): 57 M 25.