Title:
Graphically discrete groups and rigidity
Abstract:
Rigidity theorems prove that a group’s geometry determines its algebra, typically up to virtual isomorphism. Motivated by rigidity problems, we study graphically discrete groups, which impose a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds. We will present new examples in the setting of 3-manifold groups. We will discuss rigidity phenomena for free products of residually finite graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.