Polyhedral products for simplicial complexes with minimal Taylor resolutions

Abstract

We prove that for a simplicial complex $K$ whose Taylor resolution for the Stanley-Reisner ring is minimal, the following four conditions are equivalent: (1) $K$ satisfies the strong gcd-condition; (2) $K$ is Golod; (3) the moment-angle complex $\mathcal{Z}_K$ is homotopy equivalent to a wedge of spheres; (4) the decomposition of the suspension of the polyhedral product $\mathcal{Z}_K(C\underline{X},\underline{X})$ due to Bahri, Bendersky, Cohen, and Gitler desuspends.