Connected sums of sphere products and minimally non-Golod complexes

TL;DR

This paper characterizes when a moment-angle complex is a connected sum of sphere products, showing it corresponds to a join of a simplex and a minimally non-Golod complex, and answers a related open question.

Contribution

It establishes a decomposition criterion linking moment-angle complexes to minimally non-Golod complexes, providing a new structural understanding.

Findings

Identifies the conditions under which moment-angle complexes decompose into sphere products.

Proves that certain moment-angle complexes are minimally non-Golod.

Answers an open question about the structure of these 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 Grbi\'c, Panov, Theriault and Wu.