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)
@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{\textquoteright}un entrelacs},
     journal = {Annales de l'Institut Fourier},
     pages = {1229--1242},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {51},
     number = {5},
     year = {2001},
     doi = {10.5802/aif.1853},
     mrnumber = {1860664},
     zbl = {0987.57005},
     language = {fr},
     url = {http://www.numdam.org/articles/10.5802/aif.1853/}
}
TY  - JOUR
AU  - Harou, Franck
TI  - Description chirurgicale des revêtements triples simples de $S^3$ ramifiés le long d’un entrelacs
JO  - Annales de l'Institut Fourier
PY  - 2001
SP  - 1229
EP  - 1242
VL  - 51
IS  - 5
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.1853/
DO  - 10.5802/aif.1853
LA  - fr
ID  - AIF_2001__51_5_1229_0
ER  - 
%0 Journal Article
%A Harou, Franck
%T Description chirurgicale des revêtements triples simples de $S^3$ ramifiés le long d’un entrelacs
%J Annales de l'Institut Fourier
%D 2001
%P 1229-1242
%V 51
%N 5
%I Association des Annales de l’institut Fourier
%U http://www.numdam.org/articles/10.5802/aif.1853/
%R 10.5802/aif.1853
%G fr
%F AIF_2001__51_5_1229_0
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. http://www.numdam.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

Cited by Sources: