Inventiones mathematicae

, Volume 144, Issue 1, pp 169–175

Bounded cohomology and non-uniform perfection of mapping class groups

  • H. Endo
  • D. Kotschick


Using the existence of certain symplectic submanifolds in symplectic 4-manifolds, we prove an estimate from above for the number of singular fibers with separating vanishing cycles in minimal Lefschetz fibrations over surfaces of positive genus. This estimate is then used to deduce that mapping class groups are not uniformly perfect, and that the map from their second bounded cohomology to ordinary cohomology is not injective.

Mathematics Subject Classification (2000): 57R17, 57R57, 20F12 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • H. Endo
    • 1
  • D. Kotschick
    • 2
  1. 1.Department of Mathematics, Tokyo Institute of Technology, Oh-Okayama, Meguro 152-8551, Tokyo, Japan (e-mail:
  2. 2.Mathematisches Institut, Universität München, Theresienstr. 39, 80333 München, Germany (e-mail:

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