Decompositions of suspensions of spaces involving polyhedral products

TL;DR

This paper presents two new homotopy decompositions of suspensions involving polyhedral products, extending previous results and generalizing known decompositions in algebraic topology.

Contribution

It introduces two novel homotopy decompositions of suspensions with polyhedral products, broadening the understanding of their structure in algebraic topology.

Findings

Generalizes the James retractile argument for polyhedral products

Provides a decomposition on unions of diagonal subspaces

Extends previous decomposition results in the field

Abstract

Two homotopy decompositions of supensions 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 the retractile argument of James. The second decomposition is on the union of an arrangement of subspaces called diagonal subspaces, and generalizes the result of Labbasi.