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.

11 pages, the strong gcd condition deleted

References in corpus (1)

• Buchstaber numbers and classical invariants of simplicial complexes