## On the contact boundaries of normal surface singularities.(English. Abridged French version)Zbl 1080.32025

Summary: 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.

### MSC:

 32S25 Complex surface and hypersurface singularities 32S55 Milnor fibration; relations with knot theory 57R17 Symplectic and contact topology in high or arbitrary dimension

### Keywords:

rational homology sphere; contact structure
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### References:

 [1] Bădescu, L, Algebraic surfaces, (2001), Springer [2] Cantwell, J; Conlon, L, Isotopies of foliated 3-manifolds without holonomy, Adv. in math., 144, 13-49, (1999) · Zbl 0934.57033 [3] Caubel, C; Tibăr, M, Contact boundaries of hypersurface singularities and of complex polynomials, (), 29-37 · Zbl 1072.32023 [4] Giroux, E, Géométrie de contact: de la dimension trois vers LES dimensions supérieures, (), 405-414 · Zbl 1015.53049 [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] Massey, W.S, A basic course in algebraic topology, (1991), Springer · Zbl 0725.55001 [7] Milnor, J, Singular points of complex hypersurfaces, (1968), Princeton Univ. Press · Zbl 0184.48405 [8] Neumann, W, A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves, Trans. amer. math. soc., 268, 2, 299-344, (1981) · Zbl 0546.57002 [9] Pichon, A, Fibrations sur le cercle et surfaces complexes, Ann. inst. Fourier (Grenoble), 51, 2, 337-374, (2001) · Zbl 0971.32013 [10] Ustilovsky, I, Infinitely many contact structures on S4m+1, I.m.r.n., 14, 781-792, (1999) · Zbl 1034.53080 [11] Varchenko, A.N, Contact structures and isolated singularities, Moscow univ. math. bull., 35, 2, 18-22, (1980) · Zbl 0461.53022
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