21 citations · 55 across the 12 of their papers we have counts for
12 papers
Cocycles of -Alexander biquandles and -Alexander multiple conjugation biquandles
Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada +3
Biquandles and multiple conjugation biquandles are algebras which are related to links and handlebody-links in -space. Cocycles of them can be used to construct state-sum type i…
A multiple group rack and oriented spatial surfaces
Atsushi Ishii, Shosaku Matsuzaki, Tomo Murao
A spatial surface is a compact surface embedded in the 3-sphere. In this paper, we provide several typical examples of spatial surfaces and construct a coloring invariant to distin…
Biquandle (co)homology and handlebody-links
Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada +3
In this paper, we introduce the (co)homology group of a multiple conjugation biquandle. It is the (co)homology group of the prismatic chain complex, which is related to the homolog…
A multiple conjugation biquandle and handlebody-links
Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada +3
We introduce a multiple conjugation biquandle, and show that it is the universal algebra to define a semi-arc coloring invariant for handlebody-links. A multiple conjugation biquan…
Partially Multiplicative Biquandles and Handlebody-Knots
Atsushi Ishii, Sam Nelson
We introduce several algebraic structures related to handlebody-knots, including -families of biquandles, partially multiplicative biquandles and group decomposable biquandles.…
Homology for Quandles with Partial Group Operations
J. Scott Carter, Atsushi Ishii, Masahico Saito +1
A quandle is a set that has a binary operation satisfying three conditions corresponding to the Reidemeister moves. Homology theories of quandles have been developed in a way simil…