Topology/Analytic Geometry
Two-dimensional iterated torus knots and quasi-ordinary surface singularities
Comptes Rendus. Mathématique, Volume 336 (2003) no. 8, pp. 651-656.

We define a notion of 2-dimensional iterated torus knot, namely special embeddings of a 2-torus in the Cartesian product of a 2-torus and a 2-disc. We apply this definition to give a description of the embedded topology of the boundary of an irreducible quasi-ordinary hypersurface germ of dimension 2, in terms of the characteristic exponents of an arbitrary quasi-ordinary projection. Incidentally, we give an algorithm for computing the Jung–Hirzebruch type of its normalization.

Nous définissons une notion de nœud torique itéré bidimensionnel, à savoir des plongements particuliers d'un 2-tore dans le produit cartésien d'un 2-tore et d'un 2-disque. Nous appliquons cette définition à la description de la topologie plongée du bord d'un germe quasi-ordinaire irréductible d'hypersurface de dimension 2, en fonction des exposants caractéristiques d'une projection quasi-ordinaire arbitraire. Accessoirement, nous donnons un algorithme de calcul du type de Jung–Hirzebruch de sa normalisation.

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Accepted:
Published online:
DOI: 10.1016/S1631-073X(03)00099-2
Popescu-Pampu, Patrick 1

1 Univ. Paris 7 Denis Diderot, Inst. de Maths.–UMR CNRS 7586, équipe « géométrie et dynamique », case 7012, 2, place Jussieu, 75251 Paris cedex 05, France
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Popescu-Pampu, Patrick. Two-dimensional iterated torus knots and quasi-ordinary surface singularities. Comptes Rendus. Mathématique, Volume 336 (2003) no. 8, pp. 651-656. doi : 10.1016/S1631-073X(03)00099-2. http://www.numdam.org/articles/10.1016/S1631-073X(03)00099-2/

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