Commutator subgroups and toric topology
Organizers
Speaker
Fedor Vylegzhanin
Time
Tuesday, April 29, 2025 1:30 PM - 2:30 PM
Venue
A3-4-301
Online
Zoom 482 240 1589
(BIMSA)
Abstract
A right-angled Coxeter group (RACG) is generated by a set of involutions, some of which commute. It turns out that classifying spaces for RACGs and their commutator subgroups have explicit CW-models, provided by the theory of polyhedral products: those are real Davis-Januszkiewicz spaces and real moment-angle complexes, respectively. This allowed Panov and Veryovkin to give a minimal set of generators for the commutator subgroup, and to study the case when this subgroup is free. Following the idea of Li Cai, I will describe another minimal set of generators and a small sufficient set of relations between them. More generally, these results apply to Cartesian subgroups of graph products of groups.