Connected Sums of Sphere Products and Minimally Non-Golod Complexes

We show that if the moment-angle complex \(\mathcal {Z}_K\) associated with a simplicial complex K is homotopy equivalent to a connected sum of sphere products with two spheres in each product, then K decomposes as the simplicial join of an n-simplex \(\Delta ^n\) and a minimally non-Golod complex. In particular, we prove that K is minimally non-Golod for every moment-angle complex \(\mathcal {Z}_K\) homeomorphic to a connected sum of twofold products of spheres, answering a question of Grbić, Panov, Theriault and Wu.