On bind maps for braids

T. Murao*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We introduce a map, which we call the bind map, from the set of all classical braids to that of all trivalent braids. Then we define a notation for handlebody-links with a pair of a bind map and a classical braid. We show that isotopies and braid relations are equivalent for trivial handlebody-braids obtained from classical 3-braids with bind maps. We introduce two types of graphs for a classical braid, which indicate how the binding forms of the trivalent braids are transformed each other. We determine all patterns of the graphs for classical 3-braids.

Original languageEnglish
Article number1650004
JournalJournal of Knot Theory and its Ramifications
Issue number2
Publication statusPublished - 2016 Feb 1
Externally publishedYes


  • Handlebody-knot
  • braid isotopy
  • braid relation
  • trivalent braid

ASJC Scopus subject areas

  • Algebra and Number Theory


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