@article{ASNSP_2001_4_30_1_1_0, author = {Chinburg, Ted and Friedman, Eduardo and Jones, Kerry N. and Reid, Alan W.}, title = {The arithmetic hyperbolic $3$-manifold of smallest volume}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {1--40}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 30}, number = {1}, year = {2001}, zbl = {1008.11015}, mrnumber = {1882023}, language = {en}, url = {www.numdam.org/item/ASNSP_2001_4_30_1_1_0/} }
Chinburg, Ted; Friedman, Eduardo; Jones, Kerry N.; Reid, Alan W. The arithmetic hyperbolic $3$-manifold of smallest volume. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 1, pp. 1-40. http://www.numdam.org/item/ASNSP_2001_4_30_1_1_0/
[Ad] The noncompact hyperbolic 3-manifold of minimal volume, Proc. Amer. Math. Soc. 100 (1987), 601-606. | MR 894423 | Zbl 0634.57008
,[At] Lower bounds for discriminants of octic number fields having six real places, Preprint (1996).
,[BMO] The computation of sextic fields with a quadratic subfield, Math. Comp. 54 (1990), 869-884. | MR 1011438 | Zbl 0709.11056
- - ,[Bo] Commensurability classes and volumes of hyperbolic 3-manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 8 (1981), 1-33. | Numdam | MR 616899 | Zbl 0473.57003
,[Ch] A small arithmetic hyperbolic 3-manifold, Proc. Amer. Math. Soc. 100 (1987), 140-144. | MR 883417 | Zbl 0621.57006
,[CF1] The smallest arithmetic hyperbolic three-orbifold, Invent. Math. 86 (1986), 507-527. | MR 860679 | Zbl 0643.57011
- ,[CF2] Finite subgroups of maximal arithmetic subgroups of PGL(2, C), Ann. Inst. Fourier (Grenoble) 50 (2000), 1765-1798. | Numdam | MR 1817383 | Zbl 0973.20040
- ,[CF3] An embedding theorem for quaternion algebras, J. London Math. Soc. (2) 60 (1999), 33-44. | MR 1721813 | Zbl 0940.11053
- ,[CF4] Hilbert symbols, class groups and quaternion algebras, J. Théorie Nombres Bordeaux 12 (2000), 367-377. | Numdam | MR 1823190 | Zbl 0973.11097
- ,[Co] PARI, Freeware available by anonymous FTP from megrez.math.u-bordeaux.fr, directory pub/pari.
et al.,[Cu] Lifting representations to covering groups, Adv. Math. 59 (1986), 64-70. | MR 825087 | Zbl 0582.57001
,[CS1] Paradoxical decompositions, 2-generator Kleinian groups and volumes of hyperbolic 3-manifolds, J. Amer. Math. Soc. 5 (1992), 231-288. | MR 1135928 | Zbl 0769.57010
- ,[CS2] Volumes of Haken manifolds, I, Invent. Math. 118 (1994), 285-329. | MR 1292114 | Zbl 0862.57008
- ,[CS3] Varieties of group representations and splittings of 3-manifolds, Ann. of Math. 117 (1983), 109-146. | MR 683804 | Zbl 0529.57005
- ,[CHS] The first betti number of the smallest closed hyperbolic 3-manifold, Topology 37 (1998), 805-849. | MR 1607748 | Zbl 0893.57015
- - ,[EEK] Torsion free subgroups of Fuchsian groups and tessellations of surfaces, Invent. Math. 69 (1982), 331-346. | MR 679761 | Zbl 0498.20033
- - ,[GMT] Homotopy hyperbolic 3-manifolds are hyperbolic, To appear Ann. of Math. | MR 1973051 | Zbl 1052.57019
- - ,[GMMR] Arithmeticity, discreteness and volume, Trans. Amer. Math. Soc. 349 (1997), 3611-3643. | MR 1433117 | Zbl 0889.30031
- - - ,[GM] Precisely invariant collars and the volume of hyperbolic 3-folds, J. Differential Geom. 49 (1998), 411-435. | MR 1669657 | Zbl 0989.57010
- ,[Gr] "Hyperbolic Manifolds According to Thurston and Jørgensen", Séminaire Bourbaki 546, L.N.M. 842, Springer Verlag, Berlin, 1981. | Numdam | MR 636516 | Zbl 0452.51017
,[HW] Symmetries, isometries, and length spectra of closed hyperbolic 3-manifolds, Experimental Math. 3 (1994), 101-113. | MR 1341719 | Zbl 0841.57020
- ,[JRI] Minimal index torsion-free subgroups of Kleinian groups, Math. Ann. 310 (1998), 235-250. | MR 1602004 | Zbl 0890.57016
- ,[JR2] Computational methods in arithmetic Kleinian groups, in preparation.
- ,[MR1] Commensurability classes of arithmetic Kleinian groups and their Fuchsian subgroups, Math. Proc. Cambridge Philos. Soc. 102 (1987), 251-257. | MR 898145 | Zbl 0632.30043
- ,[MR2] The Arithmetic of Hyperbolic 3-Manifolds ", To appear Springer Verlag. | MR 1937957 | Zbl 1025.57001
- , "[Ma] Petits discriminants des corps de nombres, In: "Armitage", J. V. (ed.), Proceedings of the Journeés Arithmétiques 1980. London Math. Soc. Lecture Notes series 56 Cambridge Univ. Press 1982, pp. 151-193. | MR 697261 | Zbl 0491.12005
,[MV] Visualization of the isometry group action on the Fomenko Matveev Weeks manifold, J. Lie Theory 8 (1998), 51-66. | MR 1616790 | Zbl 0891.57014
- ,[Mo] Quasi-conformal mappings in n-space and the rigidity ofhyperbolic spaceforms, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 53-104. spaceforms, Inst. Hautes Etudes Sci. Publ. Math. 34 (1968), 53-104. | Numdam | MR 236383 | Zbl 0189.09402
,[O1] Corps sextiques primitifs, Ann. Inst. Fourier (Grenoble) 40 (1990), 757-767. | Numdam | MR 1096589 | Zbl 0734.11054
,[O2] The computation of sextic fields with a cubic subfield and no quadratic subfield, Math. Comp. 58 (1992), 419-432. | MR 1106977 | Zbl 0746.11041
,[Po] Sur les petits discriminants, Séminaire Delange-Pisot-Poitou, Exposé n° 6 Paris, (1976/ 77), 6-01-6-18. | Numdam | MR 551335 | Zbl 0393.12010
,[Pr] Q-rank one lattices, Invent. Math. 21 (1973), 255-286. | MR 385005 | Zbl 0264.22009
,[Prz] Cones embedded in hyperbolic 3-manifolds, Preprint (2000).
,[RW] Non-Haken 3-manifolds are not large with respect to mappings of non-zero degree, Comm. Anal. Geom. 7 (1999), 105-132. | MR 1674109 | Zbl 0930.57012
- ,[Th] "The Geometry and Topology of 3-Manifolds", Mimeographed Lecture Notes, Princeton Univ., 1977.
,[Vi] Arithmétique des algèbres de Quaternions", L.N.M. 800, Springer Verlag, Berlin, 1980. | MR 580949 | Zbl 0422.12008
, "[We1] Hyperbolic Structures on 3-manifolds", Ph. D. Thesis, Princeton University, 1985.
, "[We2] SnapPea: A computer program for creating and studying hyperbolic 3- manifolds, available by anonymous ftp from .
,