4 papers
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…
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…