Obtaining the other Alexander Polynomials

Once the Alexander-Conway polynomial has been obtained, one may proceed straight forwardly to find the other determinants that are relevant. To obtain the Greatest Common Divisor one should notice that possible factors are of the form
a t^{2k} + b t^{2k-1} + c t^{2k-2} + ... +q t^k + ... + c t^2 + b t + a
where 2(a+b+c+...)+q = \pm 1, and k.LE.n, where 2n is the power of the Alexander-Conway polynomial. In addition, a is a divisor of the constant term of the polynomial one wants to factorise. Therefore the possibilities are limited and by exhausting them one may find if there are non-trivial Alexander polynomials besides the Alexander-Conway, and their respective values. As a rule, most knots do not have non-trivial such polynomials.

To proceed with explicit results, click here.

Charilaos Aneziris, aneziris@hades.ifh.de

Copyright 1995

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