Hierarchies and Dehn Fillings for Relatively Hyperbolic Cubical Groups

Eduard Einstein
University of Illinois at Chicago
Research Assistant Professor

“Wise characterized virtually special cubical groups as groups that admit quasiconvex hierarchies terminating in finite groups. Given a relatively hyperbolic group G and a quasiconvex hierarchy for G that interacts nicely with the peripheral structure, group theoretic Dehn filling can be used to produce a hyperbolic quotient of G with an induced quasiconvex hierarchy structure. Hyperbolic virtually special groups have desirable residual properties such as residual finiteness and separability of quasiconvex subgroups, and some of these properties pull back through certain Dehn filling quotient maps. In this talk, I will discuss an application of Dehn filling used to produce a new proof of a relatively hyperbolic version of Wise’s Malnormal Special Quotient theorem and some of the ways that group theoretic Dehn filling can be used to study actions of relatively hyperbolic groups on CAT(0) cube complexes that are not necessarily proper.”