A note on Murasugi sums. (English) Zbl 0809.57003

Thompson, Abigail

Pac. J. Math. 163, No. 2, 393-395 (1994).

D. Gabai showed in [Contemp. Math. 20, 131-143 (1983; Zbl 0524.57004)] that the Murasugi sum for two knots is “natural” if performed on minimal Seifert surfaces, meaning that the genus behaves additively in this case. The authoress presents two simple examples using compressible Seifert surfaces which show that in general neither sub- additivity nor super-additivity holds for the genus under Murasugi sums.

Reviewer: G.Burde (Frankfurt / Main)

MSC:

57M25

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

Keywords:

Murasugi sum for knots; compressible Seifert surfaces

Citations:

Zbl 0524.57004