Bounded cohomology and non-uniform perfection of mapping class groups

被引：0

作者：

H. Endo

D. Kotschick

机构：

[1] Department of Mathematics,

[2] Tokyo Institute of Technology,undefined

[3] Oh-Okayama,undefined

[4] Meguro 152-8551,undefined

[5] Tokyo,undefined

[6] Japan (e-mail: endo@math.titech.ac.jp),undefined

[7] Mathematisches Institut,undefined

[8] Universität München,undefined

[9] Theresienstr. 39,undefined

[10] 80333 München,undefined

[11] Germany (e-mail: dieter@member.ams.org),undefined

来源：

Inventiones mathematicae | 2001年 / 144卷

关键词：

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

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：169 / 175

页数：6

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