Euclidean decompositions of hyperbolic manifolds and their duals

  • Epstein and Penner constructed in [EP88] the Euclidean decomposition of a non-compact hyperbolic n-manifold of finite volume for a choice of cusps, n >= 2. The manifold is cut along geodesic hyperplanes into hyperbolic ideal convex polyhedra. The intersection of the cusps with the Euclidean decomposition determined by them turns out to be rather simple as stated in Theorem 2.2. A dual decomposition resulting from the expansion of the cusps was already mentioned in [EP88]. These two dual hyperbolic decompositions of the manifold induce two dual decompositions in the Euclidean structure of the cusp sections. This observation leads in Theorems 5.1 and 5.2 to easily computable, necessary conditions for an arbitrary ideal polyhedral decomposition of the manifold to be a Euclidean decomposition.

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Author:Sascha Georg Lukac
Document Type:Book
Date of Publication (online):2007/06/22
Year of first Publication:1998
Publishing Institution:Universit├Ątsbibliothek Johann Christian Senckenberg
Release Date:2007/06/22
Dt. Fassung "Euklidische Zerlegungen hyperbolischer Mannigfaltigkeiten mit endlichem Volumen" als Diplomarbeit s.
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht