Abstract
In this chapter, we study classical discrete groups of isometries of Sn, En, and Hn. We begin with the theory of discrete reflection groups. In Section 7.4, we study the volume of an n-simplex in Sn or Hn as a function of its dihedral angles. In Section 7.5, we study the theory of crystallographic groups. The chapter ends with a proof of Selberg’s lemma.
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© 2006 Springer Science+Business Media, LLC
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(2006). Classical Discrete Groups. In: Foundations of Hyperbolic Manifolds. Graduate Texts in Mathematics, vol 149. Springer, New York, NY. https://doi.org/10.1007/978-0-387-47322-2_7
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DOI: https://doi.org/10.1007/978-0-387-47322-2_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-33197-3
Online ISBN: 978-0-387-47322-2
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