Published online by Cambridge University Press: 09 April 2009
A two-bridge knot (or link) can be characterized by the so-called Schubert normal form Kp, q where p and q are positive coprime integers. Associated to Kp, q there are the Conway polynomial ▽kp, q(z) and the normalized Alexander polynomial Δkp, q(t). However, it has been open problem how ▽kp, q(z) and Δkp, q(t) are expressed in terms of p and q. In this note, we will give explicit formulae for the Conway polynomials and the normalized Alexander polynomials in the case of two-bridge knots and links. This is done using elementary number theoretical functions in p and q.
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