TY - JOUR
T1 - The tunnel number and the cutting number with constituent handlebody-knots
AU - Murao, Tomo
N1 - Funding Information:
The author would like to express his best gratitude to Atsushi Ishii and Shin'ya Okazaki for their helpful advice and valuable discussions. This work was supported by JSPS KAKENHI Grant Number 18J10105 .
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/4/1
Y1 - 2021/4/1
N2 - 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 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.
AB - 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 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.
KW - Cutting number
KW - G-family of quandles
KW - Handlebody-knot
KW - Quandle
KW - Tunnel number
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U2 - 10.1016/j.topol.2021.107632
DO - 10.1016/j.topol.2021.107632
M3 - Article
AN - SCOPUS:85101187917
SN - 0166-8641
VL - 292
JO - Topology and its Applications
JF - Topology and its Applications
M1 - 107632
ER -