Comptes Rendus
Topology
On the degrees of branched coverings over links
[Sur les degrés des revêtements ramifiés le long d'entrelacs]
Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 169-174.

Soient M et M′ variétés tridimensionnelles et L un entrelacs dans M′. On prouve que, sous certaines conditions, le degré d'un revêtement ramifié π:M(M',L) est déterminé par les types topologiques de M et (M′,L).

Let M and M′ be 3-manifolds and L a link in M′. We prove that, under certain conditions, the degree of a branched covering π:M(M',L) is determined by the topological types of M and (M′,L).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)00023-7

António M. Salgueiro 1, 2

1 Departamento de Matemática da Universidade de Coimbra, Largo D. Dinis, 3000 Coimbra, Portugal
2 Laboratoire Émile Picard, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse, France
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António M. Salgueiro. On the degrees of branched coverings over links. Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 169-174. doi : 10.1016/S1631-073X(02)00023-7. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)00023-7/

[1] M. Boileau; J. Porti Geometrization on 3-orbifolds of cyclic type, Astérisque, Volume 272 (2000)

[2] F. Bonahon; L. Siebenmann The characteristic toric splitting of irreducible compact 3-orbifolds, Math. Ann., Volume 278 (1987), pp. 441-479

[3] W.H. Jaco; P.B. Shalen Seifert fibered spaces in 3-manifolds, Mem. Amer. Math. Soc., Volume 220 (1979)

[4] K. Johannson Homotopy Equivalences of 3-Manifolds with Boundary, Lect. Notes in Math., 761, Springer, 1979

[5] M. Kapovich Hyperbolic Manifolds and Discrete Groups, Progress in Math., 183, Birkhäuser, 2001

[6] R. Kirby Problems in low dimensional manifold theory (R.J. Milgram, ed.), Proc. Sympos. Pure Math., 32, American Mathematical Society, 1978, pp. 273-312

[7] W.H. Meeks; S.-T. Yau Topology of 3-dimensional manifolds and the embedding problems in minimal surface theory, Ann. Math., Volume 112 (1980), pp. 441-484

[8] J.-P. Otal Le théorème d'hyperbolisation pour les variétés fibrées de dimension 3, Astérisque, Volume 235 (1996)

[9] H. Seifert Topologie dreidimensionaler gefaserter Räume, Acta Math., Volume 60 (1932), pp. 147-238

[10] F. Waldhausen Eine Klasse von 3-dimensonalen Mannigfaltigkeiten I, Invent. Math., Volume 3 (1967), pp. 308-333 II, 4 (1967) 87–117

[11] S. Wang; Y.-Q. Wu Covering invariants and cohopficity of 3-manifold groups, Proc. London Math. Soc., Volume 68 (1994), pp. 203-224

[12] F. Yu; S. Wang Covering degrees are determined by graph manifolds involved, Comment. Math. Helv., Volume 74 (1999), pp. 238-247

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