J. Aust. Math. Soc.
78 (2005), 149166

Explicit formulae for twobridge knot polynomials

Shinji Fukuhara
Department of Mathematics
Tsuda College
Tsudamachi 211
Kodairashi
Tokyo 1878577
Japan
fukuhara@tsuda.ac.jp



Abstract

A twobridge knot (or link) can be characterized
by the socalled Schubert normal form where and are positive coprime integers. Associated to there are the Conway polynomial and the normalized Alexander
polynomial . However, it has been open problem how
and are expressed in terms
of and . In this note, we will give explicit formulae
for the Conway polynomials and the normalized
Alexander polynomials in the case of twobridge
knots and links. This is done using elementary
number theoretical functions in and .

Download the article in PDF format (size 124 Kb)


Australian Mathematical Publishing Association Inc.

©
Australian MS

