$\frac{n}{3}$-Neighbourly Moment-Angle Complexes and their Unstable Splittings

TL;DR

This paper investigates the conditions under which moment-angle complexes derived from $rac{n}{3}$-neighbourly simplicial complexes are co-H-spaces, linking topological properties to algebraic Golod conditions.

Contribution

It establishes a homotopy analogue of the Golod property as a criterion for moment-angle complexes to be co-H-spaces, extending understanding of their topological structure.

Findings

Moment-angle complex $ z_K$ is a co-H-space iff $K$ satisfies the homotopy Golod condition.

Provides a characterization of $rac{n}{3}$-neighbourly complexes in relation to their moment-angle complexes.

Connects combinatorial properties of $K$ with topological and algebraic properties of $ z_K$.

Abstract

Given an $\frac{n}{3}$-neighbourly simplicial complex $K$ on vertex set $[n]$, we show that the moment-angle complex $\mathcal{Z}_K$ is a $co$-$H$-space if and only if $K$ satisfies a homotopy analogue of the Golod property.