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VIDEO LIBRARY |
III International Conference "Quantum Topology"
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On volumes of compact and non-compact right-angled hyperbolic polyhedra A. Yu. Vesnin |
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Abstract: There is a recent progress in study of Platonic tessellations of a hyperbolic 3-space and related hyperbolic 3-manifolds by algorithmic topology methods [1, 2]. It is known that some of hyperbolic Platonic solids are right-angled. There we are interested in a class of hyperbolic 3-manifolds which can be decomposed into right-angled hyperbolic polyhedra. Necessary and sufficient conditions for a polyhedron of a given combinatorial type to be realized as a compact right-angled polyhedron in a hyperbolic 3-space were described by Pogorelov in 1967 in the very first issue of “Matematicheskie Zametki” (Mathematical Notes) [3]. The simplest compact right-angled hyperbolic polyhedron is a dodecahedron. The universal method to construct a hyperbolic 3-manifold from few copies of an arbitrary right-angled hyperbolic polyhedron was given in [4]. This motivates the study of the census of right-angled hyperbolic polyhedra. Recently, Inoue [5] presented 825 smallest compact right-angled hyperbolic polyhedra. We will discuss a census of non-compact right-angled hyperbolic polyhedra. For compact and non-compact cases both we will present results of numerical computations. \medskip References:
Language: English |