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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Clustering of critical points in Lefschetz fibrations and the symplectic Szpiro inequality


Authors: V. Braungardt and D. Kotschick
Journal: Trans. Amer. Math. Soc. 355 (2003), 3217-3226
MSC (2000): Primary 57R17, 57R57, 14H10
Published electronically: April 24, 2003
MathSciNet review: 1974683
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Abstract: We prove upper bounds for the number of critical points in semi- stable symplectic Lefschetz fibrations. We also obtain a new lower bound for the number of nonseparating vanishing cycles in Lefschetz pencils and reprove the known lower bounds for the commutator lengths of Dehn twists.


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Additional Information

V. Braungardt
Affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresien- strasse 39, 80333 München, Germany
Email: Volker.Braungardt@mathematik.uni-muenchen.de

D. Kotschick
Affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresien- strasse 39, 80333 München, Germany
Email: dieter@member.ams.org

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03290-2
PII: S 0002-9947(03)03290-2
Received by editor(s): September 10, 2002
Published electronically: April 24, 2003
Additional Notes: Support from the \sl Deutsche Forschungsgemeinschaft is gratefully acknowledged. The authors are members of the \sl European Differential Geometry Endeavour (EDGE), Research Training Network HPRN-CT-2000-00101, supported by The European Human Potential Programme
Article copyright: © Copyright 2003 American Mathematical Society