Loop space decompositions of highly symmetric spaces with applications to polyhedral products

TL;DR

This paper develops a method to decompose loop spaces of highly symmetric topological spaces, applying it to polyhedral products related to graphs, advancing understanding of their algebraic and topological structure.

Contribution

It generalizes the fold map for wedge sums to decompose loop spaces of symmetric spaces and applies this to polyhedral products linked to graph families.

Findings

Loop space decompositions for symmetric spaces

Application to polyhedral products of graphs

Enhanced understanding of topological structures

Abstract

We generalise the fold map for the wedge sum and use this to give a loop space decomposition of topological spaces with a high degree of symmetry. This is applied to polyhedral products to give a loop space decomposition of polyhedral products associated to families of graphs.