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arXiv · 1804.01884

The tunnel number and the cutting number with constituent handlebody-knots

Tomo Murao
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Abstract

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 handlebody-knot theory. We provide necessary conditions for constituent handlebody-knots by using $G$-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.

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Tomo Murao. 2019-04-29. The tunnel number and the cutting number with constituent handlebody-knots. https://arxiv.org/abs/1804.01884

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