For finite dimensional free $C_p$-spaces, the calculation of the Bredon cohomology ring as an algebra over the cohomology of $S^0$ is used to prove the non-existence of certain $C_p$-maps. These are related to Borsuk–Ulam type theorems, and equivariant maps related to the topological Tverberg conjecture. For certain finite dimensional $C_p$-spaces which are formed out of representations, it is proved that the cohomology is a free module over the cohomology of a point. All the calculations are done for the cohomology with constant coefficients $\mathbb{Z}/p$.

中文翻译：

---

有限维$ C_p $-空间的Bredon同调

对于有限维的自由$ C_p $-空间，布列登同调环作为$ S ^ 0 $的同调性的代数计算用于证明某些$ C_p $-映射不存在。这些与Borsuk–Ulam型定理以及与拓扑Tverberg猜想有关的等变图有关。对于由表示形式形成的某些有限维$ C_p $-空间，证明了同调是一个点的同调上的免费模块。所有计算都是针对常数系数为\\ mathbb {Z} / p $的同调进行的。