On the cohomology of the holomorph of a finite cyclic group

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.

On cohomology of crystallographic groups with cyclic holonomy of split type

We disprove a conjecture stating that the integral cohomology of any crystallographic group Z^n \rtimes Z_m is given by the cohomology of Z_m with coefficients in the cohomology of the group Z^n, by providing a complete list of counterexamples up to dimension 5. We also find a counterexample with odd order holonomy, m=9, in dimension 8 and finish the computations of the cohomology of 6-dimensional crystallographic groups arising as orbifold fundamental groups of certain Calabi-Yau toroidal orbifolds.

Cohomology of uniserial p-adic space groups with cyclic point group

Let $p$ be a fixed prime number and let $R$ denote a uniserial $p$-adic space group of dimension $d_x=(p-1)p^{x-1}$ and with cyclic point group of order $p^x$. In this short note we prove that all the quotients of $R$ of size bigger than or equal to $p^{d_x+x}$ have isomorphic mod $p$ cohomology groups. In particular, we show that the cohomology groups of sufficiently large quotients of the unique maximal class pro-$p$ group are isomorphic as $\F_p$-modules.

循环群全形的自同构群

Automorphism Group of the Holomorph of a Cyclic Group

本文证明了当阶为 $n$ 的循环群的 $n$ 为奇素数幂的两倍时，该循环群的全形同构于其自身的自同构群。

Essential Cohomology of the p-Groups with a Cyclic Subgroup of Index p

In this paper we determine explicitly the mod-p essential cohomology ideals of the p-groups with a cyclic subgroup of index p.

循环 operad 图复形的权 2 上同调与柄体群

Weight 2 cohomology of graph complexes of cyclic operads and the handlebody group

本文计算了多个循环（余）operad 费曼变换的权 2 及权 top$-2$ 上同调，利用 Giansiracusa 结果得到柄体群的权 top$-2$ 上同调，并与曲线模空间相关结果比较，还为柄体群权 top 上同调与 Kontsevich 图上同调等价提供新证明。