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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Clustering of critical points in Lefschetz fibrations and the symplectic Szpiro inequality
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by V. Braungardt and D. Kotschick PDF
Trans. Amer. Math. Soc. 355 (2003), 3217-3226 Request permission

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
  • MR Author ID: 267229
  • Email: dieter@member.ams.org
  • Received by editor(s): September 10, 2002
  • Published electronically: April 24, 2003
  • Additional Notes: Support from the Deutsche Forschungsgemeinschaft is gratefully acknowledged. The authors are members of the European Differential Geometry Endeavour (EDGE), Research Training Network HPRN-CT-2000-00101, supported by The European Human Potential Programme
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 3217-3226
  • MSC (2000): Primary 57R17, 57R57, 14H10
  • DOI: https://doi.org/10.1090/S0002-9947-03-03290-2
  • MathSciNet review: 1974683