Abstract
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.
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Further Reading
Anderson, J. (1999). Hyperbolic Geometry. Springer-Verlag, New York.
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Matsuzaki, K. and Taniguchi, M. (1998). Hyperbolic Manifolds and Kleinian Groups. Oxford University Press, Oxford.
Thurston, W. (1997). Three-Dimensional Geometry and Topology. Princeton University Press, Princeton, NJ.
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Thurston, W. (1979). The geometry and topology of three-manifolds. Notes from Princeton University.
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Maclachlan, C., Reid, A.W. (2003). Kleinian Groups and Hyperbolic Manifolds. In: The Arithmetic of Hyperbolic 3-Manifolds. Graduate Texts in Mathematics, vol 219. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-6720-9_2
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