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Surgery diagrams for horizontal contact structures

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Abstract

We describe Legendrian surgery diagrams for some horizontal contact structures on non-positive plumbing trees of oriented circle bundles over spheres with negative Euler numbers. As an application we determine Milnor fillable contact structures on some Milnor fillable 3-manifolds.

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References

  1. C. Caubel, A. Némethi and P. Popescu-Pampu, Milnor open books and Milnor fillable contact 3-manifolds, Topology, 45 (2006), 673–689.

    Article  MATH  MathSciNet  Google Scholar 

  2. T. Etgü and B. Ozbagci, Explicit horizontal open books on some plumbings, Internat. J. Math., 17 (2006), 1013–1031.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. B. Etnyre, Planar open book decompositions and contact structures, Internat. Math. Res. Notices, 79 (2004), 4255–4267.

    Article  MathSciNet  Google Scholar 

  4. J. B. Etnyre, Lectures on open book decompositions and contact structures, in: Floer Homology, Gauge Theory, and Low-dimensional Topology, Clay Math. Proc., 5, Amer. Math. Soc. (Providence, RI, 2006), pp. 103–141.

  5. J. B. Etnyre and B. Ozbagci, Open books and plumbings, Internat. Math. Res. Notices, Article ID 72710 (2006).

  6. D. Gay, Open books and configurations of symplectic surfaces, Algebr. Geom. Topol., 3 (2003), 569–586.

    Article  MATH  MathSciNet  Google Scholar 

  7. E. Giroux, Géometrie de contact: de la dimension trois vers les dimensions supérieures, in: Proceedings of the International Congress of Mathematicians, (Beijing, 2002), Vol. II, pp. 405–414.

    MathSciNet  Google Scholar 

  8. R. Gompf, Handlebody construction of Stein surfaces, Ann. of Math., 148 (1998), 619–693.

    Article  MATH  MathSciNet  Google Scholar 

  9. H. Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann., 146 (1962), 331–368.

    Article  MATH  MathSciNet  Google Scholar 

  10. K. Honda, On the classification of tight contact structures, I, Geom. Topol., 4 (2000), 309–368 (electronic).

    Article  MATH  MathSciNet  Google Scholar 

  11. P. Ozsváth and Z. Szabó, On the Floer homology of plumbed three-manifolds, Geom. Topol., 7 (2003), 185–224 (electronic).

    Article  MATH  MathSciNet  Google Scholar 

  12. B. Ozbagci and A. I. Stipsicz, Surgery on contact 3-manifolds and Stein surfaces, Bolyai Soc. Math. Stud., Vol. 13, Springer (2004).

  13. S. Schönenberger, Planar open books and symplectic fillings, Ph.D. Dissertation, University of Pennsylvania (2005).

  14. W. Thurston and H. Winkelnkemper, On the existence of contact forms, Proc. Amer. Math. Soc., 52 (1975), 345–347.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Koç University, Istanbul, Turkey

    B. Ozbagci

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  1. B. Ozbagci
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Correspondence to B. Ozbagci.

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The author was partially supported by a research grant of the Scientific and Technological Research Council of Turkey.

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Ozbagci, B. Surgery diagrams for horizontal contact structures. Acta Math Hung 120, 193–208 (2008). https://doi.org/10.1007/s10474-007-7132-0

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  • DOI: https://doi.org/10.1007/s10474-007-7132-0

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