Geometrically Finite n-Manifolds

Abstract

In this chapter, we study the geometry of geometrically finite hyperbolic n-manifolds. The chapter begins with a study of the limit set of a discrete group of Möbius transformations of B ⁿ. In Section 12.3, we study geometrically finite groups of Möbius transformations of B ⁿ. In Section 12.4, we study nilpotent groups of isometries of hyperbolic n-space. In Section 12.5, we prove the Margulis lemma. In Section 12.6, we apply the Margulis lemma to study the geometry of geometrically finite hyperbolic n-manifolds. In particular, we determine the global geometry of complete hyperbolic n-manifolds of finite volume.