The tunnel number and the cutting number with constituent handlebody-knots
The tunnel number and the cutting number with constituent handlebody-knots
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DOI：
10.1016/j.topol.2021.107632
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发表时间：
2018-04
影响因子：
0.6
通讯作者：
T. Murao
中科院分区：
文献类型：
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作者：
T. Murao
给出了隧道结点数和柄体结点数的下界。我们还给出了截割数的下界，这是柄体-结理论中隧道数的“对偶”概念。我们利用g族色浆为组成柄体结提供了必要条件。上述两个评价作为推论得到。此外，我们构造了具有任意隧道数和切割数的柄体结点。
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 handlebody-knot theory. We provide necessary conditions to be constituent handlebody-knots by usingG-family of quandles colorings. The above two evaluations are obtained as the corollaries. Furthermore, we construct handlebody-knots with arbitrary tunnel number and cutting number.