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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…
Knotted handle decomposing spheres for handlebody-knots
Atsushi Ishii, Kengo Kishimoto, Makoto Ozawa
We show that a handlebody-knot whose exterior is boundary-irreducible has a unique maximal unnested set of knotted handle decomposing spheres up to isotopies and annulus-moves. As…