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TWISTED ALEXANDER POLYNOMIAL OF A RIBBON 2-KNOT OF 1-FUSION

Kanenobu, Taizo 大阪大学 DOI:10.18910/77230

2020.10

概要

The twisted Alexander polynomial is defined as a rational function, not necessarily a polynomial. It is shown that for a ribbon 2-knot, the twisted Alexander polynomial associated to an irreducible representation of the knot group to SL(2, F) is always a polynomial. Furthermore, the twisted Alexander polynomial of a fibered ribbon 2-knot of 1-fusion has the lowest and highest degree coefficients 1 with breadth 2m − 2, where m is the breadth of its Alexander polynomial.

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