Twisted homological stability for extensions and automorphism groups of free nilpotent groups
Twisted homological stability for extensions and automorphism groups of free nilpotent groups
复制标题
自由幂零群的扩张和自同构群的扭曲同调稳定性
DOI：
10.1017/is014005031jkt267
复制
发表时间：
2014
影响因子：
--
通讯作者：
Markus Szymik
中科院分区：
文献类型：
--
作者：
Markus Szymik
我们用多项式系数证明了任何给定类的自由幂零群的自同构群的扭曲同调稳定性。这些群在同调稳定性已知的两个极端之间进行插值，即整数上的一般线性群和自由群的自同构群。这里提出的证明使用了适用于群的任意扩展的一般结果，并且也具有其他应用。
We prove twisted homological stability with polynomial coefficients for automorphism groups of free nilpotent groups of any given class. These groups interpolate between two extremes for which homological stability was known before, the general linear groups over the integers and the automorphism groups of free groups. The proof presented here uses a general result that applies to arbitrary extensions of groups, and that has other applications as well.