Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

4 Issues per year

IMPACT FACTOR 2017: 0.734

CiteScore 2017: 0.70

SCImago Journal Rank (SJR) 2017: 0.695
Source Normalized Impact per Paper (SNIP) 2017: 0.891

Mathematical Citation Quotient (MCQ) 2017: 0.62

See all formats and pricing
More options …
Volume 18, Issue 4


Canonical contact unit cotangent bundle

Takahiro Oba / Burak Ozbagci
Published Online: 2018-01-31 | DOI: https://doi.org/10.1515/advgeom-2017-0057


We describe an explicit open book decomposition adapted to the canonical contact structure on the unit cotangent bundle of a closed surface.

Keywords: Closed surface; unit cotangent bundle; contact structure; open book decomposition

MSC 2010: 53D35; 57R17


  • [1]

    N. A’Campo, Real deformations and complex topology of plane curve singularities. Ann. Fac. Sci. Toulouse Math. (6) 8 (1999), 5–23. MR1721511 Zbl 0962.32025Google Scholar

  • [2]

    D. Auroux, I. Smith, Lefschetz pencils, branched covers and symplectic invariants. In: Symplectic 4-manifolds and algebraic surfaces, volume 1938 of Lecture Notes in Math., 1–53, Springer 2008. MR2441411 Zbl 1142.14008Google Scholar

  • [3]

    K. Cieliebak, Y. Eliashberg, From Stein to Weinstein and back, volume 59 of American Mathematical Society Colloquium Publications. Amer. Math. Soc. 2012. MR3012475 Zbl 1262.32026Google Scholar

  • [4]

    P. Dehornoy, Genus-one Birkhoff sections for geodesic flows. Ergodic Theory Dynam. Systems 35 (2015), 1795–1813. MR3377285 Zbl 1352.37093Google Scholar

  • [5]

    Y. Eliashberg, Unique holomorphically fillable contact structure on the 3-torus. Internat. Math. Res. Notices (1996), no. 2, 77–82. MR1383953 Zbl 0852.58034Google Scholar

  • [6]

    Y. Eliashberg, Symplectic geometry of plurisubharmonic functions. In: Gauge theory and symplectic geometry (Montreal, PQ, 1995), volume 488 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 49–67, Kluwer 1997. MR1461569 Zbl 0881.32010Google Scholar

  • [7]

    J. B. Etnyre, Planar open book decompositions and contact structures. Int. Math. Res. Not. (2004), no. 79, 4255–4267. MR2126827 Zbl 1069.57016Google Scholar

  • [8]

    J. B. Etnyre, B. Ozbagci, Invariants of contact structures from open books. Trans. Amer. Math. Soc. 360 (2008), 3133–3151. MR2379791 Zbl 1157.57015Google Scholar

  • [9]

    E. Ghys, Right-handed vector fields & the Lorenz attractor. Jpn. J. Math. 4 (2009), 47–61. MR2491282 Zbl 1188.37028Google Scholar

  • [10]

    E. Giroux, Géométrie de contact: de la dimension trois vers les dimensions supérieures. In: Proc. International Congress of Mathematicians, Vol. II (Beijing, 2002), 405–414, Higher Ed. Press, Beijing 2002. MR1957051 Zbl 1015.53049Google Scholar

  • [11]

    R. E. Gompf, A. I. Stipsicz, 4-manifolds and Kirby calculus, volume 20 of Graduate Studies in Mathematics. Amer. Math. Soc. 1999. MR1707327 Zbl 0933.57020Google Scholar

  • [12]

    K. Honda, On the classification of tight contact structures. I. Geom. Topol. 4 (2000), 309–368. MR1786111 Zbl 0980.57010Google Scholar

  • [13]

    J. Johns, Lefschetz fibrations on cotangent bundles of two-manifolds. In: Proceedings of the Gökova Geometry-Topology Conference 2011, 53–84, Int. Press, Somerville, MA 2012. MR3076043 Zbl 1360.57032Google Scholar

  • [14]

    M. Korkmaz, B. Ozbagci, On sections of elliptic fibrations. Michigan Math. J. 56 (2008), 77–87. MR2433657 Zbl 1158.57033Google Scholar

  • [15]

    P. Massot, Topological methods in 3-dimensional contact geometry. In: Contact and symplectic topology, volume 26 of Bolyai Soc. Math. Stud., 27–83, János Bolyai Math. Soc., Budapest 2014. MR3220940 Zbl 1325.53002Google Scholar

  • [16]

    P. Massot, Two remarks on the support genus question. http://www.math.polytechnique.fr/perso/massot.patrick/exposition/genus.pdf

  • [17]

    D. McDuff, The structure of rational and ruled symplectic 4-manifolds. J. Amer. Math. Soc. 3 (1990), 679–712. MR1049697 Zbl 0723.53019Google Scholar

  • [18]

    M. McLean, Symplectic homology of Lefschetz fibrations and Floer homology of the monodromy map.Selecta Math. (N.S.) 18 (2012), 473–512. MR2960024 Zbl 1253.53084Google Scholar

  • [19]

    J. Milnor, Lectures on the h-cobordism theorem. Princeton Univ. Press 1965. MR0190942 Zbl 0161.20302Google Scholar

  • [20]

    B. Ozbagci, A. I. Stipsicz, Surgery on contact 3-manifolds and Stein surfaces, volume 13 of Bolyai Society Mathematical Studies. Springer 2004. MR2114165 Zbl 1067.57024Google Scholar

  • [21]

    P. Seidel, Fukaya categories and Picard-Lefschetz theory. European Mathematical Society, Zürich 2008. MR2441780 Zbl 1159.53001Google Scholar

  • [22]

    J. Van Horn-Morris, Constructions of open book decompositions. PhD thesis, University of Texas at Austin, 2007.Google Scholar

  • [23]

    O. Van Koert, Lecture notes on stabilization of contact open books. arXiv:1012.4359 [math.SG]Google Scholar

  • [24]

    C. Wendl, Strongly fillable contact manifolds and J-holomorphic foliations. Duke Math. J. 151 (2010), 337–384. MR2605865 Zbl 1207.32022Google Scholar

About the article

Received: 2016-02-19

Revised: 2016-07-13

Published Online: 2018-01-31

Published in Print: 2018-10-25

Funding: The first author was partially supported by JSPS KAKENHI Grant Number 15J05214.

Citation Information: Advances in Geometry, Volume 18, Issue 4, Pages 405–424, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0057.

Export Citation

© 2018 Walter de Gruyter GmbH Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in