Braid groups for ropes?

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What is the proper braid theoretic treatment of rope construction? Any are there any good references/sources? It would seem that they are something like the Artin braid group, but instead of operating on n points arranged in a straight line, it has points arranged in a circle, possibly multiple concentric circles (core, intermediate, outer sheath). But I haven't been able to find much extant exposition of it in terms of the underlying math.

Rope constructions (rope picture source )