(McGill University, CANADA)
"Groups with a quasiconvex hierarchy"
Abstract:Nonpositively curved cube complexes have become increasingly central objects in combinatorial and geometric group theory. We will survey the role that they play within the area, focusing especially on their identity as "higher dimensional graphs". We will describe a plan to use nonpositively curved cube complexes to resolve certain outstanding group theoretical problems. These include Baumslag's conjecture on the residual finiteness of one-relator groups with torsion, as well as the virtual-fibering problem for haken hyperbolic 3-manifolds.