1 citations · 1 across the 8 of their papers we have counts for
8 papers
Twisted Alexander vanishing groups of knots
Katsumi Ishikawa, Takayuki Morifuji, Masaaki Suzuki
In our previous work, we introduced the notion of a twisted Alexander vanishing (TAV) group, defined as a finite group for which the corresponding twisted Alexander polynomial of a…
Twisted Alexander polynomials of a knot for group extensions
Katsumi Ishikawa, Takayuki Morifuji, Masaaki Suzuki
In this paper, we discuss twisted Alexander polynomials of a knot for group extensions of a finite group in two directions. Firstly, we provide a mod formula for the twisted Al…
Twisted Alexander vanishing order of knots II
Katsumi Ishikawa, Takayuki Morifuji, Masaaki Suzuki
In our previous work, we introduced the notion of the twisted Alexander vanishing order of knots, defined as the order of the smallest finite group for which the corresponding twis…
Computing the associated groups of quandles with tools from group homology theory
Katsumi Ishikawa
We give a complete description of the associated group of any quandle as a central extension of the inner-automorphism group. As an application, we compute the second quandle homol…
Twisted Alexander vanishing order of knots
Katsumi Ishikawa, Takayuki Morifuji, Masaaki Suzuki
Based on a vanishing theorem for non-fibered knots due to Friedl and Vidussi, we define the twisted Alexander vanishing order of a knot to be the order of the smallest finite group…
Two-tone colorings and surjective dihedral representations for links
Kazuhiro Ichihara, Katsumi Ishikawa, Eri Matsudo +1
It is well-known that a knot is Fox -colorable for a prime if and only if the knot group admits a surjective homomorphism to the dihedral group of degree . However, this…
Quandle colorings vs. biquandle colorings
Katsumi Ishikawa, Kokoro Tanaka
Biquandles are generalizations of quandles. As well as quandles, biquandles give us many invariants for oriented classical/virtual/surface links. Some invariants derived from biqua…
Minimal coloring numbers on minimal diagrams of torus links
Kazuhiro Ichihara, Katsumi Ishikawa, Eri Matsudo
We determine the minimal number of colors for non-trivial -colorings on the standard minimal diagrams of -colorable torus links. Also included are complete…