Minimally non-Golod face rings and Massey products

Abstract

We give a correct statement and a complete proof of the criterion obtained by Grbić, Panov, Theriault and Wu for the face ring $\mathbb{k}[K]$ of a simplicial complex $K$ to be Golod over a field $\mathbb{k}$. (The original argument depended on the main result of a paper by Berglund and Jöllenbeck, which was shown to be false by Katthän.) We also construct an example of a minimally non-Golod complex $K$ such that the cohomology of the corresponding moment-angle complex ${\mathcal{Z}}_K$ has trivial cup product and a non-trivial triple Massey product.

arXiv comment3 pages