Bounded cohomology and non-uniform perfection of mapping class groups |
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| Authors: | H Endo D Kotschick |
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| Institution: | Department of Mathematics, Tokyo Institute of Technology, Oh-Okayama, Meguro 152-8551, Tokyo, Japan (e-mail: endo@math.titech.ac.jp), JP
Mathematisches Institut, Universit?t München, Theresienstr. 39, 80333 München, Germany (e-mail: dieter@member.ams.org), DE
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| Abstract: | 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.
Oblatum 8-IX-2000 & 20-X-2000?Published online: 29 January 2001 |
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| Keywords: | Mathematics Subject Classification (2000): 57R17 57R57 20F12 |
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