We introduce a new method for proving twisted homological stability, and use it to prove such results for symmetric groups and general linear groups. In addition to sometimes slightly improving the stable range given by the traditional method (due to Dwyer), it is easier to adapt to nonstandard situations. As an illustration of this, we generalize to ${GL}_n$ of many rings $R$ a theorem of Borel that says that passing from ${GL}_n$ of a number ring to a finite-index subgroup does not change the rational cohomology. Charney proved this generalization for trivial coefficients, and we extend it to twisted coefficients.

中文翻译：

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扭曲同调稳定性的新方法及其在同余子群中的应用

我们引入了一种证明扭曲同调稳定性的新方法，并用它来证明对称群和一般线性群的这种结果。除了有时稍微提高传统方法给出的稳定范围（由于Dwyer）之外，它更容易适应非标准情况。作为对此的说明，我们概括为${GL}_n$许多环的$右$Borel 定理表明，从${GL}_n$将数环转化为有限索引子群不会改变有理上同调。查尼证明了这种对平凡系数的概括，我们将其扩展到扭曲系数。