关于单纯空间的悬置分解
On decomposing suspensions of simplicial spaces
摘要：
令$X_{\bullet}$表示单纯空间。本文的目的是记录在空间$X_n$满足某些温和的拓扑假设的情况下，发生在$X_{\bullet}$中的各个空间$X_n$的悬置的分解，并且这些分解对于单纯空间的态射是自然的。此外，在一个悬浮后发生的$X_n$的被加数稳定地等价于几何实现$|X_{\bullet}|$的过滤子的选择。记录这些分解的目的是，它们意味着某些表象空间以及其他变体的单个悬置的分解，并且类似于出现在不同背景中的力矩-角度复合物的悬置的分解。
英文摘要：
Let $X_{\bullet}$ denote a simplicial space. The purpose of this note is to record a decomposition of the suspension of the individual spaces $X_n$ occurring in $X_{\bullet}$ in case the spaces $X_n$ satisfy certain mild topological hypotheses and where these decompositions are natural for morphisms of simplicial spaces. In addition, the summands of $X_n$ which occur after one suspension are stably equivalent to choices of filtration quotients of the geometric realization $|X_{\bullet}|$. The purpose of recording these decompositions is that they imply decompositions of the single suspension of certain spaces of representations as well as other varieties and are similar to decompositions of suspensions of moment-angle complexes which appear in a different context.
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