Quasi-isometry invariant subgroups

Diane Vavrichek (SUNY Binghamton)

A subgroup H of a group G is "invariant under quasi-isometries" if, for any quasi-isometry f from G to a group G', f(H) is a finite Hausdorff distance from a subgroup of G'. I will discuss recent results that give sufficient conditions for certain subgroups to be invariant under quasi-isometries.