Document Zbl 1336.57004 - zbMATH Open
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On bind maps for braids. (English) Zbl 1336.57004
Summary: 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.
MSC:
| 57M15 | Relations of low-dimensional topology with graph theory |
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
References:
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