Geometry of Discrete Groups

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


In this chapter, we study the geometry of discrete groups of isometries of S n , E n , and H n . The chapter begins with an introduction to the projective disk model of hyperbolic n-space. Convex sets, polyhedra, and polytopes in S n , E n , and H n are studied in Sections 6.2, 6.3, and 6.4, respectively. The basic properties of fundamental domains for a discrete group are examined in Sections 6.5 and 6.6. The chapter ends with a study of the basic properties of tessellations of S n , E n , and H n .


Convex Hull Convex Subset Ideal Point Discrete Group Fundamental Domain 
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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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