论文标题
通过过滤棒构造的等级过滤
The rank filtration via a filtered bar construction
论文作者
论文摘要
假设F是一个特殊的伽马空间，配备了自然转换为无限的对称功率函子。 Segal的无限环路机器与f频谱相关联，称为KF，配备了映射到Eilenberg-Mac Lane Spectrum。在以前的工作中，我们通过一系列光谱构建了KF的过滤，我们称之为“ F的稳定等级过滤”。在本文中，我们提供了稳定的级过滤的新结构。新结构本质上是组合的，避免了稳定的过程。特别是，我们构建了一系列特殊的伽马空间序列，其组完成会产生稳定的等级过滤。
Suppose F is a special Gamma-space equipped with a natural transformation to the infinite symmetric power functor. Segal's infinite loop space machine associates with F a spectrum, denoted kF, equipped with a map to the integral Eilenberg-Mac Lane spectrum. In our previous work we constructed a filtration of kF by a sequence of spectra, which we called the "stable rank filtration of F". In this paper we give a new construction of the stable rank filtration. The new construction is combinatorial in nature and avoids the process of stabilization. In particular, we construct a sequence of special Gamma-spaces whose group completion yields the stable rank filtration.
