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Clustering of critical points in Lefschetz fibrations and the symplectic Szpiro inequality
Author(s):
V.
Braungardt;
D.
Kotschick
Journal:
Trans. Amer. Math. Soc.
355
(2003),
3217-3226.
MSC (2000):
Primary 57R17, 57R57, 14H10
Posted:
April 24, 2003
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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.
References:
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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:
10.1090/S0002-9947-03-03290-2
PII:
S 0002-9947(03)03290-2
Received by editor(s):
September 10, 2002
Posted:
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
Copyright of article:
Copyright
2003,
American Mathematical Society
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