6 citations · 7 across the 14 of their papers we have counts for
14 papers
Quandle homology and relative group homology
Ayumu Inoue
We introduce a chain map from quandle homology to relative group homology, and construct several quandle cocycles through the chain map. We also relate this chain map to triangulat…
The lengths of 3-cocycles of the 7-dihedral and the octahedral quandles
Ayumu Inoue
We determine the lengths of certain 3-cocycles of the 7-dihedral and the octahedral quandles. As a consequence, we show that both of the 2-twist-spun -knot and the 4-twist-s…
A counter example of Yashiro's theorem on pseudo-cycles of a surface knot
Ayumu Inoue
We point out that the claim in Theorem 1.1 of Yashiro's paper ``Pseudo-cycles of surface-knots'' is not true, giving a counter example.
Alteration of Seifert surfaces
Ayumu Inoue
We introduce the notion of alteration of a surface embedded in a 3-manifold extending that of compression. We see that given two Seifert surfaces of the same link are related to ea…
Crossing numbers and rotation numbers of cycles in a plane immersed graph
Ayumu Inoue, Naoki Kimura, Ryo Nikkuni +1
For any generic immersion of a Petersen graph into a plane, the number of crossing points between two edges of distance one is odd. The sum of the crossing numbers of all -cycle…
The knot quandle of the twist-spun trefoil is a central extension of a Schläfli quandle
Ayumu Inoue
A quandle is an algebraic system which excels at describing limited symmetries of a space. We introduce the concept of Schläfli quandles which are defined relating to chosen rotati…
On the knot quandle of the twist-spun trefoil
Ayumu Inoue
We show that the knot quandle of the -, -, or -twist-spun trefoil is isomorphic to a quandle related to the -, -, or -cell respectively. We further show that…
On the knot quandle of a fibered knot, finiteness and equivalence of knot quandles
Ayumu Inoue
We show that the structure of a fibered knot, as a fiber bundle, is reflected in its knot quandle. As an application, we discuss finiteness and equivalence of knot quandles of conc…
A subspecies of region crossing change, region freeze crossing change
Ayumu Inoue, Ryo Shimizu
We introduce a local move on a link diagram named a region freeze crossing change which is close to a region crossing change, but not the same. We study similarity and difference b…
On colorability of knots by rotations, Torus knot and PL trochoid
Ayumu Inoue
The set consisting of all rotations of the Euclidean plane is equipped with a quandle structure. We show that a knot is colorable by this quandle if and only if its Alexander polyn…
Quasi-triviality of quandles for link-homotopy
Ayumu Inoue
We introduce the notion of quasi-triviality of quandles and define homology of quasi-trivial quandles. Quandle cocycle invariants are invariant under link-homotopy if they are asso…
Quandle homology and complex volume
Ayumu Inoue, Yuichi Kabaya
We introduce a new homology theory of quandles, called simplicial quandle homology, which is quite different from quandle homology developed by Carter et al. We construct a homomor…
A symmetric motion picture of the twist-spun trefoil
Ayumu Inoue
With the aid of a computer, we provide a motion picture of the twist-spun trefoil which exhibits the periodicity well.
Quandle and hyperbolic volume
Ayumu Inoue
We show that the hyperbolic volume of a hyperbolic knot is a quandle cocycle invariant. Further we show that it completely determines invertibility and positive/negative amphicheir…