Abstract
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 language | English |
---|---|
Article number | 1650004 |
Journal | Journal of Knot Theory and its Ramifications |
Volume | 25 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2016 Feb 1 |
Externally published | Yes |
Keywords
- braid isotopy
- braid relation
- Handlebody-knot
- trivalent braid
ASJC Scopus subject areas
- Algebra and Number Theory