Asymptotic geometry of solvable groups (with connections to dynamics)

Professor Benson Farb
University of Chicago

   We discuss the problem of determining to what extent the large-scale   geometry (i.e. quasi-isometry type) of a finitely-generated   solvable group determines its algebraic structure. We provide   an answer (joint work with Lee Mosher) in the abelian-by-cyclic case.     The proof leads from a geometry of groups problem into the theory   of Dynamical Systems via the asymptotic behavior of certain flows   and their associated foliations. This in turn leads into a    rigidity result about one-parameter subgroups of GL(n,R).