TY - JOUR

T1 - Twisted alexander polynomial of a ribbon 2-knot of 1-fusion

AU - Kanenobu, Taizo

AU - Sumi, Toshio

N1 - Funding Information:
Then since aj is expressed in a word of aj+1, aj+2,..., aj+m, and aj+m is expressed in a word of aj, aj+1,..., aj+m−1, G(K˜m)′ is a free group of rank m, completing the proof. □ Acknowledgements. The first author was partially supported by JSPS KAKENHI Grant Number JP17K05259. The second author was partially supported by JSPS KAKENHI Grant Number JP16K05151.

PY - 2020

Y1 - 2020

N2 - The twisted Alexander polynomial is defined as a rational function, not necessarily a poly-nomial. 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. Further-more, 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.

AB - The twisted Alexander polynomial is defined as a rational function, not necessarily a poly-nomial. 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. Further-more, 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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M3 - Article

AN - SCOPUS:85092531151

VL - 57

SP - 789

EP - 803

JO - Osaka Journal of Mathematics

JF - Osaka Journal of Mathematics

SN - 0030-6126

IS - 4

ER -