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Hyperbolic n-Manifolds

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

Abstract

In this chapter, we take up the study of hyperbolic n-manifolds. We begin with a geometric method for constructing spherical, Euclidean, and hyperbolic re-manifolds. In Section 11.2, we prove Poincaré’s fundamental polyhedron theorem for freely acting groups. In Section 11.3, we determine the simplices of maximum volume in hyperbolic n-space. In Section 11.4, we study the Gromov invariant of a closed, orientable, hyperbolic manifold. In Section 11.5, we study the measure homology of hyperbolic space-forms. In Section 11.6, we prove Mostow’s rigidity theorem for closed, orientable, hyperbolic manifolds.

Keywords

Hyperbolic Manifold Convex Polyhedron Fundamental Class Geodesic Line Cusp Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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