2009/04/29 by Alejandro Ádem, Adem, A., Abbas Bahri +7
Computer Science · Mathematics · #55P10 #55P40 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.0904.4699
openalex publication_date 2009/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X\bullet denote a simplicial space. The purpose of this note is to record a decomposition of the suspension of the individual spaces Xn occurring in X\bullet in case the spaces Xn satisfy certain mild topological hypotheses and where these decompositions are natural for morphisms of simplicial spaces. In addition, the summands of Xn 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.