Wedge decomposition of polyhedral products

TL;DR

This paper proves that specific polyhedral products, such as moment-angle complexes, decompose into wedges of suspension spaces for certain complexes, revealing properties of their Stanley-Reisner rings.

Contribution

It introduces a wedge decomposition for polyhedral products related to Alexander duals of shellable and Cohen-Macaulay complexes, linking topological and algebraic properties.

Findings

Polyhedral products decompose into wedges of suspension spaces.

Decomposition applies to Alexander duals of shellable and Cohen-Macaulay complexes.

Implications for Stanley-Reisner rings being Golod.

Abstract

We prove that certain polyhedral products, including the moment-angle complexes, for the Alexander duals of shellable and sequentially Cohen-Macaulay complexes decompose into wedges of explicitly given suspension spaces, which implies the properties of the Stanley-Reisner rings, known as Golod, of theses complexes.