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.

MSC Codes Primary 57M25, Secondary 57M15, 57M27

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2018 Apr 5

Keywords

  • Cutting number
  • Handlebody-knot
  • Quandle
  • Tunnel number

ASJC Scopus subject areas

  • General

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