Golod and tight 3-manifolds

TL;DR

This paper proves the equivalence of Golodness and tightness in 3-manifold triangulations by providing a topological characterization of a related polyhedral product, bridging algebraic and geometric concepts.

Contribution

It establishes the equivalence of Golodness and tightness for 3-manifold triangulations, linking algebraic and geometric properties in topology.

Findings

Golodness and tightness are equivalent for 3-manifold triangulations

Topological characterization of polyhedral products for tight-neighborly manifolds

Bridging algebraic and geometric notions in 3-manifold topology

Abstract

The notions Golodness and tightness for simplicial complexes come from algebra and geometry, respectively. We prove these two notions are equivalent for 3-manifold triangulations, through a topological characterization of a polyhedral product for a tight-neighborly manifold triangulation of dimension $\ge 3$.