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.
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.
Accepted:
Published online:
Clément Caubel 1; Patrick Popescu-Pampu 2
@article{CRMATH_2004__339_1_43_0, author = {Cl\'ement Caubel and Patrick Popescu-Pampu}, title = {On the contact boundaries of normal surface singularities}, journal = {Comptes Rendus. Math\'ematique}, pages = {43--48}, publisher = {Elsevier}, volume = {339}, number = {1}, year = {2004}, doi = {10.1016/j.crma.2004.04.023}, language = {en}, }
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/
[1] Algebraic Surfaces, Springer, 2001
[2] Isotopies of foliated 3-manifolds without holonomy, Adv. in Math., Volume 144 (1999), pp. 13-49
[3] Contact boundaries of hypersurface singularities and of complex polynomials, Geometry and Topology of Caustics – Caustics '02, Banach Center Publ., vol. 62, 2004, pp. 29-37
[4] Géométrie de contact: de la dimension trois vers les dimensions supérieures, ICM, vol. II, 2002, pp. 405-414
[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] A Basic Course in Algebraic Topology, Springer, 1991
[7] Singular Points of Complex Hypersurfaces, Princeton Univ. Press, 1968
[8] A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves, Trans. Amer. Math. Soc., Volume 268 (1981) no. 2, pp. 299-344
[9] Fibrations sur le cercle et surfaces complexes, Ann. Inst. Fourier (Grenoble), Volume 51 (2001) no. 2, pp. 337-374
[10] Infinitely many contact structures on S4m+1, I.M.R.N., Volume 14 (1999), pp. 781-792
[11] Contact structures and isolated singularities, Moscow Univ. Math. Bull., Volume 35 (1980) no. 2, pp. 18-22
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