Arithmetic Hyperbolic 3-Manifolds and Orbifolds

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

Abstract

In the preceding chapter, arithmetic Kleinian groups were defined and identified amongst all Kleinian groups. Thus several examples from earlier chapters can be reassessed as being arithmetic, thus enhancing their study. Moreover, the existence part of the classification theorem for quaternion algebras (Theorem 7.3.6) gives the existence of arithmetic Kleinian groups satisfying a variety of conditions, which, in turn, give the existence of hyperbolic 3-manifolds and orbifolds with a range of topological and geometric properties. These aspects will be explored in this chapter.

Keywords

Kleinian Group Fuchsian Group Quaternion Algebra Parabolic Element Real Place 
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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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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