Stripping and splitting decorated mapping class groups
Stripping and splitting decorated mapping class groups
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剥离和分割修饰映射类组
DOI：
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发表时间：
2001
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通讯作者：
U. Tillmann
中科院分区：
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作者：
C. Bödigheimer;U. Tillmann
我们研究了装饰映射类群，即具有标记点和边界分支的曲面的映射类群，以及它们在稳定映射下关于亏格、穿孔数目和边界分支的行为。装饰映射类群是非装饰映射类群的非平凡扩张，第一个结果指出当一个人关于亏格稳定时，扩张是同调平凡的。第二个结果表明，当关于穿孔数目和边界分支稳定时，也可以得到同调群的分裂。
We study decorated mapping class groups, i.e., mapping class groups of surfaces with marked points and boundary components, and their behaviour under stabilization maps with respect to the genus, the number of punctures and boundary components. Decorated mapping class groups are non-trivial extensions of the undecorated mapping class group, and the first result states that the extension is homologically trivial when one stabilizes with respect to the genus. The second result implies that one also gets splittings of homology groups when stabilizing with respect to the number of punctures and boundary components.