The cohomology of automorphism groups of free groups

The cohomology of automorphism groups of free groups
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自由群的自同构群的上同调

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发表时间：
2006
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通讯作者：
K. Vogtmann
K. Vogtmann
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作者：
K. Vogtmann

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有有趣的类比之间的自同构群的无规生成 一方面是自由群和曲面的映射类群，另一方面是算术群， GL（n，Z）的另一个例子。我们探讨这些类比的各个方面，侧重于上同调 特性.借助于拓扑和几何构造，研究了每一个上同调特征 与群体密切相关。这些结构常常揭示出意想不到的联系 数学的其他领域。
There are intriguing analogies between automorphism groups of finitely generated free groups and mapping class groups of surfaces on the one hand, and arithmetic groups such as GL(n, Z) on the other. We explore aspects of these analogies, focusing on cohomological properties. Each cohomological feature is studied with the aid of topological and geometric constructions closely related to the groups. These constructions often reveal unexpected connections with other areas of mathematics.