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Periodica Mathematica Hungarica

, Volume 54, Issue 1, pp 85–97 | Cite as

Brieskorn manifolds as contact branched covers of spheres

  • Ferit Öztürk
  • Klaus Niederkrüger
Article

Abstract

We show that Brieskorn manifolds with their standard contact structures are contact branched coverings of spheres. This covering maps a contact open book decomposition of the Brieskorn manifold onto a Milnor open book of the sphere.

Key words and phrases

contact branched cover Milnor open book Brieskorn manifold 

Mathematics subject classification number

53D10 57R17 

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References

  1. [A’C]
    N. A’Campo, Sur la monodromie des singularités isolées d’hypersurfaces complexes, Invent. Math., 20 (1973), 147–169. MR0338436 (49 #3201)zbMATHCrossRefMathSciNetGoogle Scholar
  2. [AO]
    S. Akbulut and B. Ozbagci, Lefschetz fibrations on compact Stein surfaces, Geom. Topol., 5 (2001), 319–334 (electronic). MR1825664 (2003a:57055)zbMATHCrossRefMathSciNetGoogle Scholar
  3. [Aur]
    D. Auroux, Symplectic 4-manifolds as branched coverings of ℂP 2, Invent. Math., 139 (2000), 551–602.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [CNP]
    C. Caubel, A. Nemethi and P. Popescu-Pampu, Milnor open books and Milnor fillable contact 3-manifolds, Topology, In Press.Google Scholar
  5. [CP]
    C. Caubel and P. Popescu-Pampu, On the contact boundaries of normal surface singularities, C. R. Math. Acad. Sci. Paris, 339 (2004), 43–48. MR2075231 (2005e:32046)zbMATHMathSciNetGoogle Scholar
  6. [Gei]
    H. Geiges, Constructions of contact manifolds, Math. Proc. Camb. Philos. Soc., 121 (1997), 455–464.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [Gir]
    E. Giroux, Géométrie de contact: De la dimension trois vers les dimensions supérieures (Contact geometry: From dimension three to higher dimensions), Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20–28, 2002. Vol. II: Invited lectures., Li, Ta Tsien (ed.), Beijing: Higher Education Press, 2002, 405–414 (in French).Google Scholar
  8. [Gon]
    J. Gonzalo, Branched covers and contact structures, Proc. Amer. Math. Soc., 101 (1987), 347–352.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [KN]
    O. van Koert and K. Niederkrüger, Open Book decompositions for contact structures on Brieskorn manifolds, Proc. Amer. Math. Soc., 133 (2005), 3679–3686.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [Mil]
    J. Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies, No. 61, Princeton University Press, Princeton, N.J., 1968. MR0239612 (39 #969)zbMATHGoogle Scholar
  11. [Ust]
    I. Ustilovsky, Infinitely many contact structures on S 4m+1, Int. Math. Res. Not., 14 (1999), 781–791.CrossRefMathSciNetGoogle Scholar

Copyright information

© Akadémiai Kiadó 2007

Authors and Affiliations

  • Ferit Öztürk
    • 1
  • Klaus Niederkrüger
    • 2
  1. 1.Department of MathematicsBoğaziçi ÜniversitesiBebek, İstanbulTurkey
  2. 2.Département de MathématiquesUniversité Libre de BruxellesBruxellesBelgium

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