论文标题
$ g_ \ infty $ - 环光谱和摩尔光谱$β$ - ring
$G_\infty$-ring spectra and Moore spectra for $β$-rings
论文作者
论文摘要
在本文中，我们介绍了$ g_ \ infty $ - 环光谱的概念。这些是具有结构化乘法的全球性同型类型，从而在其模棱两可的同型和共同体学组上产生了功率操作。我们通过分析摩尔频谱何时可以赋予$ g_ \ infty $ - 环结构来说明这种结构。这样的$ g_ \ infty $ - 结构对应于伯恩赛德环（Burnside Ring）索引的基础环上的电源操作。我们在这些全球性的功率操作与$β$ - 环的结构之间表现出密切的关系，从而为$β$ - 环的理论提供了新的观点。
In this paper, we introduce the notion of $G_\infty$-ring spectra. These are globally equivariant homotopy types with a structured multiplication, giving rise to power operations on their equivariant homotopy and cohomology groups. We illustrate this structure by analysing when a Moore spectrum can be endowed with a $G_\infty$-ring structure. Such $G_\infty$-structures correspond to power operations on the underlying ring, indexed by the Burnside ring. We exhibit a close relation between these globally equivariant power operations and the structure of a $β$-ring, thus providing a new perspective on the theory of $β$-rings.
