Quasi-Isometric Rigidity of Cusp-Decomposable Manifolds

Abstract

In this paper we explore coarse properties of cusp-decomposable manifolds defined in [Pha12]. We describe the large scale geometry of the universal cover of a cusp-decomposable manifold and of quasiisometries between two such universal covers. This description will provide us the tools to prove quasi-isometric rigidity for fundamental groups of cusp-decomposable manifolds.