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 group of Möbius transformations of Bn. In Sections 12.2 and 12.3, we study the limit set of a discrete group of Möbius transformations of Bn. In Section 12.4, we study geometrically finite groups of Möbius transformations of Bn. In Section 12.5, we study nilpotent groups of isometries of hyperbolic n-space. In Section 12.6, we prove the Margulis lemma. In Section 12.7, 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.
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© 2006 Springer Science+Business Media, LLC
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(2006). Geometrically Finite n-Manifolds. In: Foundations of Hyperbolic Manifolds. Graduate Texts in Mathematics, vol 149. Springer, New York, NY. https://doi.org/10.1007/978-0-387-47322-2_12
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DOI: https://doi.org/10.1007/978-0-387-47322-2_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-33197-3
Online ISBN: 978-0-387-47322-2
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