关于Sp（p-1，Z[1/n]）的Farrell上同调的p-周期性

一类辫群的中心与一类纯映射类群的Farrell上同调

The center of some braid groups and the Farrell cohomology of certain pure mapping class groups

本文首先证明了许多低亏格曲面的辫群的中心是它们的直接因子。然后，利用商曲面的基本群的自同构群，给出了球面商曲面的纯映射类群中素阶元的中心化子和正规化子的描述.作为应用，我们证明了某些映射类群的Farrell上同调群的$p$ -准素部分是初等的阿贝尔群.最后计算了几个纯映射类群的Farrell上同调的$p$ -准素部分。

群上同调中的广义周期性

Generalized Periodicity in Group Cohomology

本文通过引入“编码对”推广有限群的周期上同调理论，并推广Swan定理的上同调条件，该定理涉及周期上同调群在球面上的自由作用。

The cohomology ring of certain families of periodic virtually cyclic groups

Let G be a virtually cyclic of the form (Z_a x Z_b) x Z or [Z_a x (Z b x Q_{2^i})] x Z. We compute the integral cohomology ring of G, and then obtain the periodicity of the Farell cohomology of these groups.

Periodicity in the cohomology of finite general linear groups via q-divided powers

We show that $\bigoplus_{n \ge 0} {\mathrm H}^t({\bf GL}_n({\bf F}_q), {\bf F}_\ell)$ canonically admits the structure of a module over the $q$-divided power algebra (assuming $q$ is invertible in ${\bf F}_{\ell}$), and that, as such, it is free and (for $q \neq 2$) generated in degrees $\le t$. As a corollary, we show that the cohomology of a finitely generated ${\bf VI}$-module in non-describing characteristic is eventually periodic in $n$. We apply this to obtain a new result on the cohomology of unipotent Specht modules.