Fixed point sets of group actions on euclidean space
Fixed point sets of group actions on euclidean space
复制标题
欧几里得空间上群动作的不动点集
DOI：
10.1016/0040-9383(75)90018-x
复制
发表时间：
1975
期刊：
影响因子：
--
通讯作者：
Ronnie Lee
中科院分区：
文献类型：
--
作者：
A. Edmonds;Ronnie Lee
如果上面的r是素数幂，那么PA Smith理论会说，M一定是Z-非循环的，因此是非紧的，或者只是一点。在文献[61]中，Conner和Ee Floyd首先构造了无不动点的欧氏空间上的Z作用的例子。GE Bredon[3，pp.58-621]观察到它们的构造推广到产生具有任何有限同伦型的非紧不动点集的作用。因此，我们的贡献是确定什么紧致流形可以发生，回答了Smith[7，p.4121]的一个问题。作为我们工作的副产品，我们还展示了
If r above were a prime power then PA Smith theory would say that M must be Z-acyclic and hence be non-compact or just one point. In [61 PE Conner and EE Floyd first constructed examples of Z, actions on euclidean space with no fixed points. GE Bredon [3, pp. 58-621 has observed that their construction generalizes to produce actions with non-compact fixed point set of any finite homotopy type. Thus our contribution is to determine what compact manifolds can occur, answering a question of Smith [7, p. 4121. As a by-product of our work we also show