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, pp. 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: 10.5802/aif.1853
Classification: 20F36, 57M12, 57M25, 57N10
Mot clés : 3-variété, revêtement ramifié, chirurgie, entrelacs, tresse
Keywords: 3-manifold, branched cover, surgery, link, braid
Harou, Franck 1

1 Université de Rennes 1, IRMAR, Campus de Beaulieu, 35042 Rennes Cedex (France)
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Harou, Franck. 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/articles/10.5802/aif.1853/

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

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

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

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

[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., Volume 80 (1974), pp. 845-846 | DOI | MR | Zbl

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

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

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

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

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

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