4 papers
math.GT2026
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…
math.GT2025
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.
math.GT2025
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…
math.GT2025
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…