Geodesic
Separable closed braids
Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 521-531 
G. S. Makanin. Separable closed braids. Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 521-531. http://geodesic.mathdoc.fr/item/SM_1988_60_2_a16/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The structure of separable closed braids is described. It is proved that for every separable braid with $n+1$ threads and length of expression $d$ one can indicate an equivalent separated closed braid whose length of expression does not exceed $(d+2)(n+1)n$. Bibliography: 3 titles.

[1] Artin E., “Theorie der Zopfe”, Abh. math. Semin. Univ. Hamburg, 4 (1925), 47–72 | DOI | Zbl

[2] Garside F. A., “On the braid group and other groups”, Quart. J. Math. Oxford., 20:78 (1969), 235–254 | DOI | MR | Zbl

[3] Makanin G. S., “O normalizatorakh gruppy kos”, Matem. sb., 86(28) (1971), 171–179 | MR | Zbl