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Explore a 41-minute lecture on commanding subgroups presented by Sam Shepherd at the Workshop on Cube Complexes and Combinatorial Geometry. Delve into the intricacies of constructing finite covers of graphs of spaces/groups, focusing on the creation of finite-index subgroups within vertex groups that intersect edge groups in a controlled manner. Examine the concept of a group commanding a collection of subgroups, with emphasis on virtually special cubulated groups. Gain insights into practical applications, including an exploration of quasi-isometric rigidity. This talk, part of the Atelier sur complexes cubiques et géométrie combinatoire, was hosted by the Centre de recherches mathématiques (CRM) in June 2023.
