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

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.