Decompositions of suspensions of spaces involving polyhedral products (Q276579)

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)].