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Braided chord diagrams. (English) Zbl 0896.57003

The authors are interested in finite type invariants for knots and braids. In particular, they hope to find examples which would prove that finite type invariants detect non-invertibility for knots. They call the conjecture that such examples exist the NIC (non-invertibility conjecture). In this paper, they develop a method of possible approach for that conjecture and obtain some partial results. For that purpose, they introduce and study the notion of a braided chord diagram and give an equivalence relation which identifies all braidings of a fixed chord diagram. They show that finite type invariants are stratified by braid index for knots which can be represented as closed 3-braids and they obtain partial results about spanning sets for the algebra of chord diagrams for braid index 3.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
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