Connected sums of sphere products and minimally non-Golod complexes

Abstract

We show that if the moment-angle complex ${\mathcal{Z}}_K$ associated to 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 two-fold products of spheres, answering a question of Grbić, Panov, Theriault and Wu.

9 pages. Comments welcome