Bounded cohomology and non-uniform perfection of mapping class groups
Bounded cohomology and non-uniform perfection of mapping class groups
复制标题
映射类群的有界上同调和非均匀完备性
DOI：
10.1007/s002220100128
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发表时间：
2000
影响因子：
3.1
通讯作者：
D. Kotschick
中科院分区：
文献类型：
--
作者：
Hisaaki Endo;D. Kotschick
摘要：利用辛 4 流形中某些辛子流形的存在性，我们证明了对正属表面上最小 Lefschetz 纤维中具有分离消失循环的奇异纤维数量的估计。然后使用该估计来推断映射类群不是一致完美的，并且从它们的第二有界上同调到普通上同调的映射不是单射的。
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.