Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Fillable contact structures on torus bundles over circles

Author: Piotr Mikrut
Journal: Proc. Amer. Math. Soc. 130 (2002), 599-607
MSC (1991): Primary 57M60, 53C15.
Published electronically: July 25, 2001
MathSciNet review: 1862144
Full-text PDF

Abstract | References | Similar Articles | Additional Information


We will construct an example of a strongly symplectically fillable contact structure on a torus bundle over the circle with parabolic monodromy.

References [Enhancements On Off] (What's this?)

  • [ABKLR] B.Aebischer, M.Borer, M.Kälin, Ch.Leuenberger, H.M.Reimann, Symplectic Geometry, Birkhäuser Basel, Boston, Berlin, (1994). MR 96a:58082
  • [BPV] W.Barth, C.Peters, A.Van der Ven, Compact Complex Surfaces, Springer-Verlag (1984). MR 86c:32026
  • [BS] Uga Bruzzo, Guido Sanguinetti, Mirror symmetry on K3 surfaces as a hyper-Käeler rotation, Lett.Math.Phys. 45 (1998), 295-301. MR 99k:14064
  • [Et] John B.Etnyre, Symplectic convexity in low-dimensional topology, Proceedings of the Georgia Conference Topology Conference (1996), Topology and its Applications 88 no. 1-2 (1998), 3-25. MR 99j:57014
  • [El1] Y.Eliashberg,, Unique holomorphically fillable contact structures on the 3-torus, Int. Math. Res. Notices 2 (1996), 77-82. MR 97b:53034
  • [Gi1] E.Giroux, Une structure de contact, meme tendue est plus ou moins tordue, Ann. Scient. Ec. Norm. Sup. 27 (1994), 697-705. MR 96b:57034
  • [Ka] Y.Kanda, The classification of tight contact structures on the 3-torus, Comm. Anal. Geom. 5 (1997), 413-438. MR 99c:57054
  • [M] J.Martinet, Formes de contact sur les variétés de dimension 3, Springer Lecture Notes in Math. 209, (1971), 142-163. MR 50:3263
  • [Mi] P.Mikrut, Invariant contact structure on 3-manifolds with local actions of tori, preprint.
  • [NTZ] Nguyen-Tien-Zung, Symplectic topology of integrable Hamiltonian systems, I: Arnold-Liouville with singularities, Compositio Mathematica, 101 (1996), 179-215. MR 97c:58052
  • [O] T.Oda, Lectures on torus embeddings and its applications, Springer-Verlag, Tata Institute of Fundamental Research, Bombay (1978). MR 81e:14001

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57M60, 53C15.

Retrieve articles in all journals with MSC (1991): 57M60, 53C15.

Additional Information

Piotr Mikrut
Affiliation: Mathematical Institute, University of Wrocław, pl.Grunwaldzki 2/4, 50-384 Wrocław, Poland

Keywords: 3-manifold, torus bundle, contact structure, tight contact structure, fillable contact structure, integrable systems
Received by editor(s): April 21, 2000
Received by editor(s) in revised form: July 31, 2000
Published electronically: July 25, 2001
Additional Notes: The author was partially supported by the Polish Committee of Scientific Research grant 2 P03A 023 14
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society