Graphically discrete groups and rigidity
De Emily Stark
One type of rigidity theorem proves that a group’s geometry determines its algebra, typically up to virtual isomorphism. We study graphically discrete groups, which impose a discreteness criterion on the automorphism group of any graph the group acts on geometrically. It follows that if a graphically discrete group acts geometrically on the same locally finite graph as another group, then the two are virtually isomorphic. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds. We will present new examples and demonstrate this property is not a quasi-isometry invariant. We will discuss rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.