Kleinian Groups and Hyperbolic Manifolds
As indicated in the Preface, this book is written for those with a reasonable knowledge of Kleinian groups and hyperbolic 3-manifolds, with the aim of extending their repertoire in this area to include the applications and implications of algebraic number theory to the study of these groups and manifolds.This chapter includes the main ideas and results on Kleinian groups and hyperbolic 3-manifolds, which will be used subsequently. There are no proofs in this chapter and we assume that the reader has at least a passing knowledge of some of the ideas expounded here. In the Further Reading at the the end of the chapter, references are given for all the results that appear here so that deficiencies in the presentation here may be remedied from these sources.
KeywordsFundamental Domain Hyperbolic Manifold Kleinian Group Parabolic Element Ideal Vertex
Unable to display preview. Download preview PDF.
- Beardon, A. (1983). The Geometry of Discrete Groups. Graduate Texts in Mathematics Vol. 91. Springer-Verlag, New York.Google Scholar
- Vinberg, E., editor (1993b). Geometry II (II). Encyclopaedia of Mathematical Sciences Vol. 29. Springer-Verlag, Berlin.Google Scholar
- Hempel, J. (1976). 3-Manifolds. Annals of Mathematics Studies Vol. 86. Princeton University Press, Princeton, NJ.Google Scholar
- Jaco, W. (1980). Lectures on Three-Manifold Topology. AMS Conference Series No. 43. American Mathematical Society, Providence, RI.Google Scholar
- Neumann, W. and Reid, A. (1992a). Arithmetic of hyperbolic manifolds. In Topology ‘80 pages 273–310, Berlin. de Gruyter.Google Scholar
- Mostow, G. (1973). Strong Rigidity of Locally Symmetric Spaces. Annals of Mathematics Studies. Princeton University Press, Princeton, NJ.Google Scholar