Decompositions of suspensions of spaces involving polyhedral products
type: Item
instance of: scholarly article
title: Decompositions of suspensions of spaces involving polyhedral products
zbMATH Open document ID: 1341.55002
author: Kouyemon Iriye
author: Daisuke Kishimoto
published in: Algebraic \& Geometric Topology
publication date: 2016-05-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1505.04889
Mathematics Subject Classification ID: 55P15
Mathematics Subject Classification ID: 55U10
Mathematics Subject Classification ID: 52C35
zbMATH DE Number: 6577068
zbMATH Keywords: homotopy decomposition
zbMATH Keywords: polyhedral products
zbMATH Keywords: retractile spaces over posets
zbMATH Keywords: diagonal arrangements
reviewed by: Miguel Ottina
MaRDI profile type: Publication
OpenAlex ID: W2269366852
arXiv ID: 1505.04889
DOI: 10.2140/AGT.2016.16.825
review text: This article deals with homotopy decompositions of the suspensions of certain spaces. Two families of spaces are studied.NEWLINENEWLINEFirst, the authors give a homotopy decomposition of the suspension of the colimit of a functor from a graded lower semilattice to the category of pointed topological spaces under suitable assumptions. This homotopy decomposition generalizes the homotopy decomposition of a suspension of a polyhedral product given in [\textit{A. Bahri et al.}, Adv. Math. 225, No. 3, 1634--1668 (2010; Zbl 1197.13021)]. In particular, it generalizes the classical homotopy decomposition of the suspension of a product of spaces.NEWLINENEWLINEThen the authors give a homotopy decomposition for the suspensions of diagonal arrangements (which include the braid arrangement as a particular case). This generalizes a result of [\textit{F. Labassi}, J. Homotopy Relat. Struct. 10, No. 3, 375--400 (2015; Zbl 1329.55020)].
description: scientific article; zbMATH DE number 6577068