Configuration Spaces and Polyhedral Products

TL;DR

This paper investigates the conditions under which moment-angle complexes are co-H-spaces, exploring the conjecture that Golod simplicial complexes yield such structures, using advanced configuration space techniques.

Contribution

It establishes the most general combinatorial criteria for moment-angle complexes to be co-H-spaces, extending the understanding of their topological splitting properties.

Findings

Identifies conditions for moment-angle complexes to be co-H-spaces

Provides partial validation of the Golod conjecture in specific cases

Develops a generalized theory of labelled configuration spaces

Abstract

This paper aims to find the most general combinatorial conditions under which a moment-angle complex $(D^2,S^1)^K$ is a co-$H$-space, thus splitting unstably in terms of its full subcomplexes. In this way we study to which extent the conjecture holds that a moment-angle complex over a Golod simplicial complex is a co-$H$-space. Our main tool is a certain generalisation of the theory of labelled configuration spaces.