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

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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 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.

Original languageEnglish
Article number107632
JournalTopology and its Applications
Volume292
DOIs
Publication statusPublished - 2021 Apr 1

Keywords

  • Cutting number
  • G-family of quandles
  • Handlebody-knot
  • Quandle
  • Tunnel number

ASJC Scopus subject areas

  • Geometry and Topology

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