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.
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© 1994 Springer Science+Business Media New York
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Ratcliffe, J.G. (1994). Hyperbolic n-Manifolds. In: Foundations of Hyperbolic Manifolds. Graduate Texts in Mathematics, vol 149. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4013-4_11
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DOI: https://doi.org/10.1007/978-1-4757-4013-4_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94348-0
Online ISBN: 978-1-4757-4013-4
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