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.


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