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math.GT2018★ 1 cited
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…
math.GT2018★ 1 cited
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…