论文标题
固定点集和基本组I：对G-CW复合物的半无动作
Fixed Point Sets and the Fundamental Group I: Semi-free Actions on G-CW-Complexes
论文作者
论文摘要
史密斯理论说，对于任何主要因子$ p $ of $ g $，$ g $ $ g $在合同空间上的半无动作动作的固定点为$ {\ bb z} _p $ -asyclic。琼斯证明了史密斯理论的相反案例$ g $是一个循环群，该群体作用于有限的CW-复合物。我们将理论扩展到对给定同质类型的有限CW复合物的半群体作用，在各种设置中。尤其是，史密斯理论的相反是在且仅当某些$ k $理论的障碍物消失时才存在。我们还举了一些例子，以显示不同类型的$ K $理论障碍的效果。
Smith theory says that the fixed point of a semi-free action of a group $G$ on a contractible space is ${\bb Z}_p$-acyclic for any prime factor $p$ of $G$. Jones proved the converse of Smith theory for the case $G$ is a cyclic group acting on finite CW-complexes. We extend the theory to semi-free group action on finite CW-complexes of given homotopy type, in various settings. In particular, the converse of Smith theory holds if and only if certain $K$-theoretical obstruction vanishes. We also give some examples that show the effects of different types of the $K$-theoretical obstruction.
