Geodesic
Hyperbolic 3-Manifolds with Geodesic Boundary: Enumeration and Volume Calculation
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 167-183

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TM_2006_252_a14,
     author = {A. D. Mednykh and C. Petronio},
     title = {Hyperbolic {3-Manifolds} with {Geodesic} {Boundary:} {Enumeration} and {Volume} {Calculation}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {167--183},
     publisher = {mathdoc},
     volume = {252},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_252_a14/}
}
TY  - JOUR
AU  - A. D. Mednykh
AU  - C. Petronio
TI  - Hyperbolic 3-Manifolds with Geodesic Boundary: Enumeration and Volume Calculation
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2006
SP  - 167
EP  - 183
VL  - 252
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2006_252_a14/
LA  - en
ID  - TM_2006_252_a14
ER  - 
%0 Journal Article
%A A. D. Mednykh
%A C. Petronio
%T Hyperbolic 3-Manifolds with Geodesic Boundary: Enumeration and Volume Calculation
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2006
%P 167-183
%V 252
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2006_252_a14/
%G en
%F TM_2006_252_a14
A. D. Mednykh; C. Petronio. Hyperbolic 3-Manifolds with Geodesic Boundary: Enumeration and Volume Calculation. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 167-183. http://geodesic.mathdoc.fr/item/TM_2006_252_a14/