Polyhedral products and commutator subgroups of right-angled Artin and Coxeter groups

TL;DR

This paper develops polyhedral product models for classifying spaces of right-angled Artin and Coxeter groups, providing new criteria for freeness and explicit generators for their commutator subgroups.

Contribution

It introduces polyhedral product models for these groups and their subgroups, offering new tools for understanding their algebraic and topological properties.

Findings

Criterion for the freeness of commutator subgroups

Explicit minimal generators for right-angled Coxeter groups

Polyhedral models for classifying spaces

Abstract

We construct and study polyhedral product models for classifying spaces of right-angled Artin and Coxeter groups, general graph product groups and their commutator subgroups. By way of application, we give a criterion of freeness for the commutator subgroup of a graph product group, and provide an explicit minimal set of generators for the commutator subgroup of a right-angled Coxeter group.