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Open book decompositions for contact structures on Brieskorn manifolds
Author(s):
Otto
van Koert;
Klaus
Niederkrüger
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3679-3686.
MSC (2000):
Primary 53D10
Posted:
June 8, 2005
MathSciNet review:
2163607
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Abstract:
In this paper, we give an open book decomposition for the contact structures on some Brieskorn manifolds, in particular for the contact structures of Ustilovsky. The decomposition uses right-handed Dehn twists as conjectured by Giroux.
References:
-
- 1.
- E. Brieskorn, Beispiele zur Differentialtopologie von Singularitäten, Invent. Math. 2 (1966), 1-14. MR 0206972 (34:6788)
- 2.
- H. Geiges, Contact geometry, to appear in the Handbook of Differential Geometry, vol. 2, Elsevier, arXiv:math.SG/0307242.
- 3.
- E. Giroux, Géométrie de contact: de la dimension trois vers les dimensions supérieures, Proceedings of the International Congress of Mathematicians, Vol. II (Beijing), Higher Ed. Press, 2002, pp. 405-414. MR 1957051 (2004c:53144)
- 4.
- E. Giroux and J-P. Mohsen, Contact structures and symplectic fibrations over the circle, lecture notes.
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- F. Hirzebruch and K. H. Mayer,
 -Mannigfaltigkeiten, exotische Sphären und Singularitäten, Lecture Notes in Mathematics, No. 57, Springer-Verlag, Berlin, 1968. MR 0229251 (37:4825) - 6.
- R. Lutz and C. Meckert, Structures de contact sur certaines sphères exotiques, C. R. Acad. Sci. Paris Sér. A-B 282 (1976), no. 11, Aii, A591-A593. MR 0397612 (53:1471)
- 7.
- P. Seidel, Symplectic automorphisms of
 , arXiv:math.DG/9803084. - 8.
- I. Ustilovsky, Infinitely many contact structures on
 , Internat. Math. Res. Notices (1999), no. 14, 781-791. MR 1704176 (2000f:57028)
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Additional Information:
Otto
van Koert
Affiliation:
Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50.931 Köln, Federal Republic of Germany
Email:
okoert@mi.uni-koeln.de
Klaus
Niederkrüger
Affiliation:
Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50.931 Köln, Federal Republic of Germany
Email:
kniederk@mi.uni-koeln.de
DOI:
10.1090/S0002-9939-05-07944-X
PII:
S 0002-9939(05)07944-X
Keywords:
Contact geometry,
Dehn twists
Received by editor(s):
June 21, 2004
Received by editor(s) in revised form:
August 16, 2004
Posted:
June 8, 2005
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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