论文标题
添加功率操作
Additive power operations in equivariant cohomology
论文作者
论文摘要
让$ g $为有限的组，$ e $是$ h_ \ infty $ -ring $ g $ -spectrum。 For any $G$-space $X$ and positive integer $m$, we give an explicit description of the smallest Mackey ideal $\underline{J}$ in $\underline{E}^0(X\times BΣ_m)$ for which the reduced $m$th power operation $\underline{E}^0(X) \to \underline{E}^0(X \times BΣ_m ）/\下划线{j} $是绿色函子的地图。我们将此结果作为普通定理的特殊情况，我们在$ g \timesς_m$ -green函数的上下文中建立。当$ e $是超出共同的全局环频谱时，该定理还专门描述适当的理想$ \下划线{j} $。我们为球形频谱，复杂的$ K $ - 理论和Morava $ e $ - 理论提供了示例计算。
Let $G$ be a finite group and $E$ be an $H_\infty$-ring $G$-spectrum. For any $G$-space $X$ and positive integer $m$, we give an explicit description of the smallest Mackey ideal $\underline{J}$ in $\underline{E}^0(X\times BΣ_m)$ for which the reduced $m$th power operation $\underline{E}^0(X) \to \underline{E}^0(X \times BΣ_m )/\underline{J}$ is a map of Green functors. We obtain this result as a special case of a general theorem that we establish in the context of $G\timesΣ_m$-Green functors. This theorem also specializes to characterize the appropriate ideal $\underline{J}$ when $E$ is an ultra-commutative global ring spectrum. We give example computations for the sphere spectrum, complex $K$-theory, and Morava $E$-theory.
