Hyperbolic 3-manifolds with geodesic boundary: Enumeration and volume calculation |
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Authors: | A. D. Mednykh C. Petronio |
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Affiliation: | (1) Sobolev Institute of Mathematics, Russian Academy of Sciences, pr. akad. Koptyuga 4, Novosibirsk, 630090, Russia;(2) Dipartimento di Matematica Applicata, Università di Pisa, Via Bonanno Pisano 25B, 56126 Pisa, Italy |
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Abstract: | 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 hyperbolic space. |
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