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

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.

16 pages. Minor changes, additions and corrections in this version

References in corpus (1)

• On the fundamental group of certain polyhedral products

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• Equivariant cohomology of moment-angle complexes with respect to coordinate subtori
• Zoo of monotone Lagrangians in $\mathbb{C}{P}^n$