Fillable contact structures on torus bundles over circles

Mikrut, Piotr

doi:10.1090/S0002-9939-01-06119-6

Fillable contact structures on torus bundles over circles
HTML articles powered by AMS MathViewer

by Piotr Mikrut

Proc. Amer. Math. Soc. 130 (2002), 599-607

DOI: https://doi.org/10.1090/S0002-9939-01-06119-6

Published electronically: July 25, 2001

PDF | Request permission

Abstract:

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

References

B. Aebischer, M. Borer, M. Kälin, Ch. Leuenberger, and H. M. Reimann, Symplectic geometry, Progress in Mathematics, vol. 124, Birkhäuser Verlag, Basel, 1994. An introduction based on the seminar in Bern, 1992. MR 1296462, DOI 10.1007/978-3-0348-7512-7
W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 4, Springer-Verlag, Berlin, 1984. MR 749574, DOI 10.1007/978-3-642-96754-2
Ugo Bruzzo and Guido Sanguinetti, Mirror symmetry on $K$3 surfaces as a hyper-Kähler rotation, Lett. Math. Phys. 45 (1998), no. 4, 295–301. MR 1653424, DOI 10.1023/A:1007446916202
John B. Etnyre, Symplectic convexity in low-dimensional topology, Topology Appl. 88 (1998), no. 1-2, 3–25. Symplectic, contact and low-dimensional topology (Athens, GA, 1996). MR 1634561, DOI 10.1016/S0166-8641(97)00196-X
Yasha Eliashberg, Unique holomorphically fillable contact structure on the $3$-torus, Internat. Math. Res. Notices 2 (1996), 77–82. MR 1383953, DOI 10.1155/S1073792896000074
Emmanuel Giroux, Une structure de contact, même tendue, est plus ou moins tordue, Ann. Sci. École Norm. Sup. (4) 27 (1994), no. 6, 697–705 (French, with English summary). MR 1307678
Yutaka Kanda, The classification of tight contact structures on the $3$-torus, Comm. Anal. Geom. 5 (1997), no. 3, 413–438. MR 1487723, DOI 10.4310/CAG.1997.v5.n3.a2
J. Martinet, Formes de contact sur les variétés de dimension $3$, Proceedings of Liverpool Singularities Symposium, II (1969/1970), Lecture Notes in Math., Vol. 209, Springer, Berlin, 1971, pp. 142–163 (French). MR 0350771
P.Mikrut, Invariant contact structure on 3-manifolds with local actions of tori, preprint.
Nguyen Tien Zung, Symplectic topology of integrable Hamiltonian systems. I. Arnold-Liouville with singularities, Compositio Math. 101 (1996), no. 2, 179–215. MR 1389366
Tadao Oda, Torus embeddings and applications, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 57, Tata Institute of Fundamental Research, Bombay; Springer-Verlag, Berlin-New York, 1978. Based on joint work with Katsuya Miyake. MR 546291