Polyhedral products and commutator subgroups of right-angled Artin and Coxeter groups. (English. Russian original) Zbl 1397.20040
Sb. Math. 207, No. 11, 1582-1600 (2016); translation from Mat. Sb. 207, No. 11, 105-126 (2016).
Summary: 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 for the commutator subgroup of a graph product group to be free, and provide an explicit minimal set of generators for the commutator subgroup of a right-angled Coxeter group.
MSC:
| 20F36 | Braid groups; Artin groups |
| 20F55 | Reflection and Coxeter groups (group-theoretic aspects) |
| 20F65 | Geometric group theory |
| 20F12 | Commutator calculus |
| 55R35 | Classifying spaces of groups and \(H\)-spaces in algebraic topology |
| 57M07 | Topological methods in group theory |
