On asymptotic cones and quasi-isometry classes of fundamental groups of 3-manifolds (Q1895260)

The concept of asymptotic cone is applied to distinguish quasi-isometry classes of fundamental groups of 3-manifolds. It is proved that the existence of a Seifert component in a Haken manifold is a quasi-isometry invariant of its fundamental group. Results of this paper are used in the subsequent paper [the authors, Quasi-isometries preserve the geometric decomposition of Haken manifolds, Preprint, 1995] to prove quasi-isometry invariance of geometric decomposition of Haken manifolds and to describe finitely-generated groups which are quasi-isometric to fundamental groups of closed Haken 3-manifolds.