Hyperbolic 3-Manifolds

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


In this chapter, we construct some examples of hyperbolic 3-manifolds. We begin with a geometric method for constructing spherical, Euclidean, and hyperbolic 3-manifolds in Sections 10.1 and 10.2. Examples of complete hyperbolic 3-manifolds of finite volume are constructed in Section 10.3. The problem of computing the volume of a hyperbolic 3-manifold is taken up in Section 10.4. The chapter ends with a detailed study of hyperbolic Dehn surgery on the figure-eight knot complement.


Dihedral Angle Hyperbolic Structure Cusp Point Ideal Vertex Dehn Surgery 
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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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