10 citations · 22 across the 9 of their papers we have counts for
9 papers
(Co)homology of racks and multiple group racks for compact oriented surfaces in the 3-sphere
Shosaku Matsuzaki, Tomo Murao
We introduce (co)homology theory for multiple group racks and construct cocycle invariants of compact oriented surfaces in the 3-sphere using their 2-cocycles, where a multiple gro…
Circle arrangements of link projections
Noboru Ito, Shosaku Matsuzaki, Kouki Taniyama
An oriented link projection is the image of a generic immersion of oriented circles into the 2-sphere. The circle arrangement of a link projection is a disjoint union of unoriented…
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…
A diagrammatic presentation and its characterization of non-split compact surfaces in the 3-sphere
Shosaku Matsuzaki
We give a presentation for a non-split compact surface embedded in the 3-sphere by using diagrams of spatial trivalent graphs equipped with signs and we define Reidemeister moves f…
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…
Genera and minors of multibranched surfaces
Shosaku Matsuzaki, Makoto Ozawa
We say that a -dimensional CW complex is a multibranched surface if we remove all points whose open neighborhoods are homeomorphic to the -dimensional Euclidean space, then w…
An obstruction to embedding -dimensional complexes into the -sphere
Kazufumi Eto, Shosaku Matsuzaki, Makoto Ozawa
We consider an embedding of a -dimensional CW complex into the -sphere, and construct it's dual graph. Then we obtain a homogeneous system of linear equations from the -di…