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A calculus on links in the 3-sphere. (English) Zbl 0764.57005

Knots 90, Proc. Int. Conf. Knot Theory Rel. Topics, Osaka/Japan 1990, 625-631 (1992).
[For the entire collection see Zbl 0747.00039.]
This paper gives an overview of a series of papers by the authors entitled “Studying links via closed braids, I-VI” [see Zbl 0724.57001, Zbl 0722.57001, Zbl 0711.57006, Zbl 0758.57005, Zbl 0739.57002 — Part III has not been reviewed up to now]. The principal goal is to find moves on \(n\)-string braids which can be used to replace the Markov moves so that braids representing the same links can be shown to be related by a sequence of moves which do not increase the number of strings. They introduce an ‘exchange move’ which goes some way to fulfilling the desired role.

MSC:

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