Groups of Isometries

  • Bernard Maskit
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 287)


In this chapter we describe the three basic geometries, elliptic, parabolic, and primarily hyperbolic, that are important for the theory of Kleinian groups. We then build some of the theory of discrete groups of isometries in these geometries. The major results are the construction of the Dirichlet and Ford regions, and the proof of Poincare’s polyhedron theorem.


Discrete Subgroup Kleinian Group Hyperbolic Geometry Perpendicular Bisector Inside Boundary 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Bernard Maskit
    • 1
  1. 1.Dept. of MathematicsSUNY at Stony BrookStony BrookUSA

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