Two-dimensional Golod complexes

TL;DR

This paper characterizes two-dimensional Golod complexes both combinatorially and topologically, and explores differences in Golodness over fields and rings, revealing complexes with unique topological properties.

Contribution

It provides a combinatorial and topological characterization of two-dimensional Golod complexes and demonstrates the existence of simple Golod complexes with non-suspension moment-angle complexes.

Findings

Characterization of Golod complexes via vertex-breakability and fat-wedge filtration

Identification of differences in Golodness over fields and rings

Existence of simple Golod complexes with non-suspension moment-angle complexes

Abstract

We characterize two-dimensional Golod complexes combinatorially by vertex-breakability and topologically by the fat-wedge filtration of a polyhedral product. Applying the characterization, we consider a difference between Golodness over fields and rings, which enables us to give a two-dimensional simple Golod complex over any field such that the corresponding moment-angle complex is not a suspension.