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Bounded cohomology and non-uniform perfection of mapping class groups

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 نشر من قبل D. Kotschick
 تاريخ النشر 2000
  مجال البحث
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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.



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