论文标题
投影模块和$（g，n）$ - 复合物的同型分类
Projective modules and the homotopy classification of $(G,n)$-complexes
论文作者
论文摘要
$（g，n）$ - 复合体是一个$ n $ dimensional cw-complex，带有基本组$ g $，其通用封面为$（n-1）$ - 连接。如果$ g $具有定期的共同体学，那么，对于适当的$ n $，我们表明，在有限$（g，n）$ - 复合物的同型类型之间存在一对一的对应关系，而在$ \ text of $ \ text text aut aut aut {aut} $下，某个投射$ \ mathbb {z} g $ - module的稳定类别的轨道。我们开发了明确计算此操作的技术，并以此为例，在动作不平凡的情况下。
A $(G,n)$-complex is an $n$-dimensional CW-complex with fundamental group $G$ and whose universal cover is $(n-1)$-connected. If $G$ has periodic cohomology then, for appropriate $n$, we show that there is a one-to-one correspondence between the homotopy types of finite $(G,n)$-complexes and the orbits of the stable class of a certain projective $\mathbb{Z} G$-module under the action of $\text{Aut}(G)$. We develop techniques to compute this action explicitly and use this to give an example where the action is non-trivial.
