Two homotopy decompositions of suspensions of spaces involving polyhedral products are given. The first decomposition is motivated by the decomposition of suspensions of polyhedral products by Bahri, Bendersky, Cohen and Gitler, and is a generalization of a retractile argument of James. The second decomposition is on the union of an arrangement of subspaces called diagonal subspaces, and generalizes a result of Labassi.
"Decompositions of suspensions of spaces involving polyhedral products." Algebr. Geom. Topol. 16 (2) 825 - 841, 2016. https://doi.org/10.2140/agt.2016.16.825