Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Fillable contact structures on torus bundles over circles

Author(s): Piotr Mikrut
Journal: Proc. Amer. Math. Soc. 130 (2002), 599-607.
MSC (1991): Primary 57M60, 53C15.
Posted: July 25, 2001
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract:

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

References:

[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 Wroclaw, pl.Grunwaldzki 2/4, 50-384 Wroclaw, Poland
Email: mikrut@math.uni.wroc.pl

DOI: 10.1090/S0002-9939-01-06119-6
PII: S 0002-9939(01)06119-6
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
Posted: 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
Copyright of article: Copyright 2001, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google