1 citations · 1 across the 5 of their papers we have counts for
8 papers · 1 filter
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…
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 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…