Isometries of Hyperbolic Space

  • John G. Ratcliffe
Part of the Graduate Texts in Mathematics book series (GTM, volume 149)


In this chapter, we study the topology of the group I(H n ) of isometries of hyperbolic space. The chapter begins with an introduction to topological groups. The topological group structure of I(H n ) is studied from various points of view in Section 5.2. The discrete subgroups of I(H n ) are of fundamental importance for the study of hyperbolic manifolds. The basic properties of the discrete subgroups of I(H n ) are examined in Section 5.3. A characterization of the discrete subgroups of I(E n ) is given in Section 5.4. The chapter ends with a characterization of all the elementary discrete subgroups of I(H n ).


Normal Subgroup Topological Group Hyperbolic Space Discrete Group Finite Index 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • John G. Ratcliffe
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

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