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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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Signature of relations in mapping class groups and non-holomorphic Lefschetz fibrations
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by Hisaaki Endo and Seiji Nagami PDF
Trans. Amer. Math. Soc. 357 (2005), 3179-3199 Request permission

Abstract:

We introduce the notion of signature for relations in mapping class groups and show that the signature of a Lefschetz fibration over the 2-sphere is the sum of the signatures for basic relations contained in its monodromy. Combining explicit calculations of the signature cocycle with a technique of substituting positive relations, we give some new examples of non-holomorphic Lefschetz fibrations of genus $3, 4$ and $5$ which violate slope bounds for non-hyperelliptic fibrations on algebraic surfaces of general type.
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Additional Information
  • Hisaaki Endo
  • Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
  • Email: endo@math.wani.osaka-u.ac.jp
  • Seiji Nagami
  • Affiliation: 3-6-3-10 Sakuranchou, Toyonaka, Osaka 560-0054, Japan
  • Email: nagami-s@est.hi-ho.ne.jp
  • Received by editor(s): November 16, 2003
  • Published electronically: September 2, 2004

  • Dedicated: Dedicated to Professor Yukio Matsumoto for his 60th birthday
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 3179-3199
  • MSC (2000): Primary 57R20; Secondary 57N13, 20F05, 14D06
  • DOI: https://doi.org/10.1090/S0002-9947-04-03643-8
  • MathSciNet review: 2135741