基于过滤条结构的秩过滤
The rank filtration via a filtered bar construction
摘要：
设F是一个特殊的Gamma-空间，具有到无穷对称幂函子的自然变换.西格尔的无限闭路空间机将F与一个谱相关联，记为kF，配有一个到积分艾伦伯格-麦克莱恩谱的映射。在我们以前的工作中，我们通过一系列谱构造了kF的过滤，我们称之为“F的稳定秩过滤”。本文给出了稳定秩滤子的一种新构造。新的结构本质上是组合的，避免了稳定化过程。特别地，我们构造了一个特殊的伽玛空间序列，其群完成产生稳定的秩过滤。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
