Topology and its Applications 264 233-250 2019 [Refereed]

A coherent band surgery is a local move of an oriented knot or link by doing a surgery along an added band. The coherent band-Gordian distance between two links is the minimum number of coherent band surgeries needed to transform one into the othe...

COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY 33(2) 591-604 2018 [Refereed]

We consider a family of ribbon 2-knots with trivial Alexan- der polynomial. We give nonabelian SL(2,C)-representations from the groups of these knots, and then calculate the twisted Alexander polyno- mials associated to these representations, whic...

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 26(8) Jul 2017 [Refereed]

We enumerate ribbon 2-knots presented by virtual arc diagrams with up to four classical crossings. We use a linear Gauss diagram for a virtual arc diagram.

Twisted Alexander polynomial of a ribbon 2-knot[Invited]

Taizo Kanenobu

The 14th East Asian Conference on Geometric Topology 22 Jan 2019

The twisted Alexander polynomial is 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 pol...

Twisted Alexander polynomial of a ribbon 2-knot

Taizo Kanenobu

5 Sep 2018

Twisted Alexander polynomial of a ribbon 2-knot of 1-fusion[Invited]

Taizo Kanenobu

The 10th KOOK-TAPU Joint Seminar on Knots and Related Topics 26 Jul 2018

In general, the twisted Alexander polynomial is a rational function, not necessarily a polynomial. It is shown that for a ribbon 2-knot of 1-fusion, the twisted Alexander polynomial associated to a irreducible representation of the knot group to S...

Classification of a family of ribbon 2-knots with trivial Alexander polynomial[Invited]

Taizo KANENOBU

The 13th East Asian School of Knots and Related Topics 30 Jan 2018

We consider a family of ribbon 2-knots with trivial Alexander polynomial. We give nonabelian -representations from the groups of these knots, and then calculate the twisted Alexander polynomials associated to these representations, which ...

Coherent band-Gordian distances between knots and links with up to seven crossings[Invited]

Taizo KANENOBU

The 2nd Pan Pacific International Conference on Topology and Applications 16 Nov 2017 Pusan National University