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Труды Математического института имени В. А. Стеклова, 2006, том 252, страницы 167–183
(Mi tm70)
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Hyperbolic 3-Manifolds with Geodesic Boundary: Enumeration and Volume Calculation
A. D. Mednykha, C. Petroniob a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b University of Pisa
Аннотация:
We describe a natural strategy to enumerate compact hyperbolic 3-manifolds with geodesic boundary in increasing order of complexity. We show that the same strategy can be applied in order to analyze simultaneously compact manifolds and finite-volume manifolds with toric cusps. In contrast, we show that if one allows annular cusps, the number of manifolds grows very rapidly and our strategy cannot be employed to obtain a complete list. We also carefully describe how to compute the volume of our manifolds, discussing formulas for the volume of a tetrahedron with generic dihedral angles in a hyperbolic space.
Поступило в ноябре 2004 г.
Образец цитирования:
A. D. Mednykh, C. Petronio, “Hyperbolic 3-Manifolds with Geodesic Boundary: Enumeration and Volume Calculation”, Геометрическая топология, дискретная геометрия и теория множеств, Сборник статей, Труды МИАН, 252, Наука, МАИК «Наука/Интерпериодика», М., 2006, 167–183; Proc. Steklov Inst. Math., 252 (2006), 155–171
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/tm70 https://www.mathnet.ru/rus/tm/v252/p167
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