Abstract
As an application of the construction of open books on plumbed 3-manifolds, we construct elliptic open books on torus bundles over the circle. In certain cases these open books are compatible with Stein fillable contact structures and have minimal genus.
Similar content being viewed by others
References
Alexander J. (1923). A lemma on systems of knotted curves. Proc. Nat. Acad. Sci. USA 9: 93–95
Etnyre, J.: Planar open books and contact structures. Int. Math. Res. Not. 4255–4267 (2004)
Etgü T. and Ozbagci B. (2006). Explicit horizontal open books on some plumbings. Internat. J. Math. 17: 1013–1031
Gay D. (2003). Open books and configurations of symplectic surfaces. Algebr. Geom. Topol. 3: 569–586
Gay D. (2006). Four-dimensional symplectic cobordisms containing three-handles. Geom. Topol. 10: 1749–1759
Giroux E. (2000). Structures de contact en dimension trois et bifurcations des feuilletages de surfaces. Invent. Math. 141: 615–689
Giroux, E.: Géometrie de contact: de la dimension trios vers les dimensions supérieures. Proceedings of the International Congress of Mathematicians, vol. 2, pp. 405–414. Beijing (2002)
Honda K. (2000). On the classification of tight contact structures II. J. Differential Geom. 55: 83–143
Honda K., Kazez W. and Matic G. (2007). Right-veering diffeomorphisms of compact surfaces with boundary Invent. Math. 169: 427–449
Kirby R. and Melvin P. (1994). Dedekind sums, μ-invariants and the signature cocyle. Math. Ann. 299: 231–267
Korkmaz, M., Ozbagci, B.: On sections of elliptic fibrations. Michigan Math. J. (to appear), arXiv:math.GT/0604516
Martinet, J.: Formes de contact sur les variétés de dimension 3. In: Proc. Liverpool Singularity Sympos. II, Lecture Notes in Math. 209, pp. 142–163. Springer, Berlin (1971)
Ozsváth, P., Stipsicz, A., Szabó, Z.: Planar open books and Floer homology. Int. Math. Res. Not. 3385–3401 (2005)
Rolfsen D.: Knots and links. Publish or Perish (1976)
Thurston W.P. and Winkelnkemper H.E. (1975). On the existence of contact forms. Proc. Amer. Math. Soc. 52: 345–347
Van Horn-Morris, J.: Ph.D. Dissertation, University of Texas at Austin, (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Etgü, T. Elliptic open books on torus bundles over the circle. Geom Dedicata 132, 53–63 (2008). https://doi.org/10.1007/s10711-007-9171-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10711-007-9171-7