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.
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