Meridional generators and plat presentations of torus links

by Markus Rost and Heiner Zieschang (12 pages)

J. London Math. Soc. (2) 35 (1987), no. 3, 551-562.

MR 889376, Zbl 587.57005.

For the torus link t(a,b) the bridge-number and the minimal number of meridional (Wirtinger) generators necessary to generate the knot group coincide and are equal to min (|a|,|b|). Moreover, any two minimal plat presentations of t(a,b) are algebraically equivalent.

(ab,a^2ba^{-1},...,a^qba^{1-q})

Links to journal: Journal of the London Mathematical Society · Oxford University Press

This is actually my first paper. Published in 1987, the results were obtained in Summer 1983 (my last year as a student and in Bochum).

Décompositions de Heegaard des extérieurs des noeuds toriques et des variétés de Seifert associées

by Michel Boileau, Markus Rost, and Heiner Zieschang (4 pages)

C. R. Acad. Sci. Paris Sér. I Math. 302 (1986), no. 18, 661-664

Article (Gallica).

MR 847514, Zbl 596.57009.

On Heegaard decompositions of torus knot exteriors and related Seifert fibre spaces

by Michel Boileau, Markus Rost, and Heiner Zieschang (29 pages)

Math. Ann. 279 (1988), no. 3, 553-581.

MR 922434, Zbl 616.57008.

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