Comptes Rendus
no. 1
Differential Topology/Analytic Geometry
On the contact boundaries of normal surface singularities
[Sur les bords de contact des singularités de surfaces normales]

Présenté par : Étienne Ghys

Clément Caubel1 ; Patrick Popescu-Pampu2
1 5, rue Henri Poincaré, 75020 Paris, France
2 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
Comptes Rendus. Mathématique, Volume 339 (2004) no. 1, pp. 43-48.

Le bord abstrait M d'une singularité analytique complexe de surface normale est canoniquement muni d'une structure de contact. Nous montrons que si M est une sphère d'homologie rationnelle, alors cette structure de contact est uniquement déterminée par le type topologique de M. Un outil essentiel est la notion de livre ouvert portant une structure de contact, définie par E. Giroux.

The abstract boundary M of a normal complex-analytic surface singularity is canonically equipped with a contact structure. We show that if M is a rational homology sphere, then this contact structure is uniquely determined by the topological type of M. An essential tool is the notion of open book carrying a contact structure, defined by E. Giroux.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.04.023
Clément Caubel 1 ; Patrick Popescu-Pampu 2

1 5, rue Henri Poincaré, 75020 Paris, France
2 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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     language = {en},
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Clément Caubel; Patrick Popescu-Pampu. On the contact boundaries of normal surface singularities. Comptes Rendus. Mathématique, Volume 339 (2004) no. 1, pp. 43-48. doi : 10.1016/j.crma.2004.04.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.04.023/

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[5] E. Giroux, Contact structures and symplectic fibrations over the circle, Notes of the Summer School “Holomorphic Curves and Contact Topology”, Berder, June 2003; Available at: http://www-fourier.ujf-grenoble.fr/~eferrand/berder.html

[6] W.S. Massey A Basic Course in Algebraic Topology, Springer, 1991

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