Golodness and polyhedral products for two dimensional simplicial complexes

TL;DR

This paper investigates Golodness in 2-dimensional simplicial complexes using polyhedral products, providing combinatorial and topological characterizations, and addresses a question about rational Golodness versus Golod over finite fields.

Contribution

It offers new characterizations of Golodness for surface triangulations and answers a question about differences in Golodness over rationals and finite fields.

Findings

Characterization of Golodness for surface triangulations

Existence of complexes rationally Golod but not Golod over _p

Insights into polyhedral products in 2D simplicial complexes

Abstract

Golodness of 2-dimensional simplicial complexes is studied through polyhedral products, and combinatorial and topoogical characterization of Golodness of surface triangulations is given. An answer to the question of Berglund is also given so that there is a 2-dimensional simplicial complex which is rationally Golod but is not Golod over $\mathbb{Z}/p$.