论文标题
无平方顺序循环基团的模糊共同体
Equivariant cohomology for cyclic groups of square-free order
论文作者
论文摘要
本文的主要目的是计算$ r（g）$ - 分级的共同体，$ g $ - 孔的组$ g = c_n $，其中$ n $是独特的素数的产物。我们为常量的Mackey Foundor $ \ USWINELLINE {Z} $计算这些组，并为Burnside Ring Mackey Foundor $ \ useverline {a} $计算这些组。除其他事项外，我们表明$ \ upessuess {h}^α_g（s^0）$主要由虚拟表示$α$的固定点维确定，除非$ \ useverline {a} $系数在固定点尺寸为$α$时具有许多zeros。在$ \下划线{z} $系数的情况下，还描述了同时组上的环结构。然后，该计算用于证明某些$ g $复合物的freeness结果。
The main objective of this paper is to compute $RO(G)$-graded cohomology of $G$-orbits for the group $G=C_n$, where $n$ is a product of distinct primes. We compute these groups for the constant Mackey functor $\underline{Z}$ and for the Burnside ring Mackey functor $\underline{A}$. Among other things, we show that the groups $\underline{H}^α_G(S^0)$ are mostly determined by the fixed point dimensions of the virtual representations $α$, except in the case of $\underline{A}$ coefficients when the fixed point dimensions of $α$ have many zeros. In the case of $\underline{Z}$ coefficients, the ring structure on the cohomology is also described. The calculations are then used to prove freeness results for certain $G$-complexes.
