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.
MSC Codes Primary 57M25, Secondary 57M15, 57M27
|Publication status||Published - 2018 Apr 5|
- Cutting number
- Tunnel number
ASJC Scopus subject areas