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
     

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
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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.

5.
F. Hirzebruch and K. H. Mayer, ${\rm O}(n)$-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 $T^*S^2$, arXiv:math.DG/9803084.

8.
I. Ustilovsky, Infinitely many contact structures on $S\sp {4m+1}$, Internat. Math. Res. Notices (1999), no. 14, 781-791. MR 1704176 (2000f:57028)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53D10

Retrieve articles in all Journals with MSC (2000): 53D10

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.

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