论文标题
固定点集和基本组II：Euler特征
Fixed Point Sets and the Fundamental Group II: Euler Characteristics
论文作者
论文摘要
对于一组$ g $的非主要电力订单，奥利弗（Oliver）表明，有限的CW-Complex $ f $的障碍物是合可能的有限有限$ g $ -CW-Complex的固定点集，是Euler特性$χ（f）$。他也对紧凑型谎言小组行动也有类似的结果。我们表明，$ f $的类似问题是某些给定同型类型的有限$ g $ -cw-complex的固定点集仍然由Euler特性确定。使用$ k_0 $中的跟踪地图，我们还看到基本组和固定点集的组件结构有有趣的角色。
For a group $G$ of not prime power order, Oliver showed that the obstruction for a finite CW-complex $F$ to be the fixed point set of a contractible finite $G$-CW-complex is the Euler characteristic $χ(F)$. He also has the similar results for compact Lie group actions. We show that the analogous problem for $F$ to be the fixed point set of a finite $G$-CW-complex of some given homotopy type is still determined by the Euler characteristic. Using trace maps in $K_0$, we also see that there are interesting roles for the fundamental group and the component structure of the fixed point set.
