Kleinian Groups and Hyperbolic Manifolds

  • Colin Maclachlan
  • Alan W. Reid
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 219)

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.

Keywords

Fundamental Domain Hyperbolic Manifold Kleinian Group Parabolic Element Ideal Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Further Reading

  1. Anderson, J. (1999). Hyperbolic Geometry. Springer-Verlag, New York.MATHGoogle Scholar
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Colin Maclachlan
    • 1
  • Alan W. Reid
    • 2
  1. 1.Department of Mathematical Sciences, Kings CollegeUniversity of AberdeenAberdeenUK
  2. 2.Department of MathematicsUniversity of Texas at AustinAustinUSA

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