Groups of Isometries
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.
KeywordsDiscrete Subgroup Kleinian Group Hyperbolic Geometry Perpendicular Bisector Inside Boundary
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