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- W2795962711 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." @default.
- W2795962711 created "2018-04-13" @default.
- W2795962711 creator A5085863646 @default.
- W2795962711 date "2018-04-05" @default.
- W2795962711 modified "2023-09-23" @default.
- W2795962711 title "The tunnel number and the cutting number with constituent handlebody-knots" @default.
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- W2795962711 doi "https://doi.org/10.48550/arxiv.1804.01884" @default.
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