Link genus and the Conway moves. (English) Zbl 0693.57004

Scharlemann, Martin; Thompson, Abigail

Comment. Math. Helv. 64, No. 4, 527-535 (1989).

The authors study the relation between the degrees of the Conway potential functions and the maximal Euler characteristic of all Seifert surfaces for a link. Two consequences of their work are: (a) a lower bound for the height of the Conway skein diagram; (b) characterization of doubled knots as those with genus and unknotting number equal to 1.

Reviewer: L.P.Neuwirth

MSC:

57M25

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

Keywords:

Conway potential; Seifert surfaces; link; skein diagram; unknotting number