Quasisymmetric universality, quasi-isometric classification and topological rigidity of Kleinian groups

Abstract

We study the quasisymmetric classification of limit sets of Kleinian groups and obtain a characterization of those geometrically finite limit sets that are quasisymmetrically universal. This allows us to obtain a quasi-isometric classification of finitely generated Kleinian groups. We also obtain a classification of virtually topologically rigid geometrically finite Kleinian groups.

arXiv comment87 pages, 24 figures