一种扭同调稳定性的新方法及其在同余子群上的应用

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2023-11-21 DOI:10.1112/topo.12316

Andrew Putman

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引用次数: 6

摘要

本文介绍了一种新的证明扭同调稳定性的方法，并用它证明了对称群和一般线性群的扭同调稳定性。除了有时会略微提高传统方法给出的稳定范围(由于Dwyer)外，它更容易适应非标准情况。为了说明这一点，我们将Borel的一个定理推广到GL n$ \operatorname{GL}_n$的多环R$ R$，该定理表明从一个数环的GL n$ \operatorname{GL}_n$传递到有限索引子群并不改变有理上同。Charney证明了对平凡系数的推广，我们把它推广到扭曲系数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A new approach to twisted homological stability with applications to congruence subgroups

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.

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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.