Description chirurgicale des revêtements triples simples de S 3 ramifiés le long d’un entrelacs  [ Surgery description of simple three folds cover of the 3-sphere branched along a link ]
Annales de l'Institut Fourier, Volume 51 (2001) no. 5, p. 1229-1242
We present an algorithm for converting a branched cover description of a 3-manifold into a description by surgery.
Nous présentons un algorithme permettant de convertir une présentation de variété de dimension 3 comme revêtement simple à trois feuillets de la sphère en une présentation de chirurgie.
DOI : https://doi.org/10.5802/aif.1853
Classification:  20F36,  57M12,  57M25,  57N10
Keywords: 3-manifold, branched cover, surgery, link, braid
@article{AIF_2001__51_5_1229_0,
     author = {Harou, Franck},
     title = {Description chirurgicale des rev\^etements triples simples de $S^3$ ramifi\'es le long d'un entrelacs},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {51},
     number = {5},
     year = {2001},
     pages = {1229-1242},
     doi = {10.5802/aif.1853},
     mrnumber = {1860664},
     zbl = {0987.57005},
     language = {fr},
     url = {https://aif.centre-mersenne.org/item/AIF_2001__51_5_1229_0}
}
Description chirurgicale des revêtements triples simples de $S^3$ ramifiés le long d’un entrelacs. Annales de l'Institut Fourier, Volume 51 (2001) no. 5, pp. 1229-1242. doi : 10.5802/aif.1853. https://aif.centre-mersenne.org/item/AIF_2001__51_5_1229_0/

[1] J. Birman Braids, links and mapping class groups, Univ. Press, Princeton, Annals of Math. Studies, Tome vol. 84 (1975) | MR 425944 | Zbl 0305.57013

[2] J. Birman; B. Wajnryb 3-fold branched coverings and the mapping class group of a surface, Springer-Verlag, Lecture Note, Tome 1167 (1985) | MR 827260 | Zbl 0589.57009

[3] G. Burde; H. Zieschang Knots, De Gruyter, Studies in Math., Tome vol. 5 (1985) | MR 808776 | Zbl 0568.57001

[4] P. Dehornoy A fast method for comparing braids, Adv. Math., Tome 125 (1997) no. 2, pp. 200-235 | Article | MR 1434111 | Zbl 0882.20021

[5] F. Harou (2000) (Thèse de Doctorat, Université de Rennes 1)

[6] J. Montesinos A representation of closed orientable 3-manifolds as 3-fold branched coverings of S 3 , Bull. Amer. Soc., Tome 80 (1974), p. 845-846 | Article | MR 358784 | Zbl 0292.57003

[7] J. Montesinos; 1975 Surgery on links and double branched covers of S 3 , Knots, Groups and 3-Manifolds, Univ. Press, Princeton (Ann. Math. Stud.) Tome vol. 84 (227-259) | Zbl 0325.55004

[8] J. Montesinos Three-manifolds as 3-fold branched covers of S 3 , Quart. J. Math. Oxford, Tome 27 (1976) no. 2, pp. 85-90 | Article | MR 394630 | Zbl 0326.57002

[9] V.V. Prasolov; A.B. Sossinsky Knots, Links, Braids and 3-manifolds, AMS Trans., Springer-Verlag, Math. Monograph, Tome vol. 154 (1997) | Zbl 0864.57002

[10] D. Rolfsen Knots and links, Publish or Perish (1977) | MR 1277811 | Zbl 0339.55004

[11] P. Vogel Representation of links by braids : a new algorithm, Comment. Math. Helv., Tome 65 (1990) no. 1, pp. 104-113 | Article | MR 1036132 | Zbl 0703.57004