9 citations · 11 across the 8 of their papers we have counts for
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(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…
Affine extensions of multiple conjugation quandles and augmented MCQ Alexander pairs
Tomo Murao
A multiple conjugation quandle is an algebra whose axioms are motivated from handlebody-knot theory. Any linear extension of a multiple conjugation quandle can be described by usin…
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…
Linear extensions of multiple conjugation quandles and MCQ Alexander pairs
Tomo Murao
A quandle is an algebra whose axioms are motivated from knot theory. A linear extension of a quandle can be described by using a pair of maps called an Alexander pair. In this pape…
The tunnel number and the cutting number with constituent handlebody-knots
Tomo Murao
We give lower bounds for the tunnel number of knots and handlebody-knots. We also give a lower bound for the cutting number, which is a "dual" notion to the tunnel number in the ha…
A relationship between multiple conjugation quandle/biquandle colorings
Tomo Murao
We define a functor from the category of multiple conjugation biquandles to that of multiple conjugation quandles. We show that for any multiple conjugation biquandle…
The Gordian distance of handlebody-knots and Alexander biquandle colorings
Tomo Murao
We give lower bounds for the Gordian distance and the unknotting number of handlebody-knots by using Alexander biquandle colorings. We construct handlebody-knots with Gordian dista…
On connected component decompositions of quandles
Yusuke Iijima, Tomo Murao
We give a formula of the connected component decomposition of the Alexander quandle: , where $a=\…