The arithmetic hyperbolic 3-manifold of smallest volume
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 30 (2001) no. 1, p. 1-40 
@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},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 30},
     number = {1},
     year = {2001},
     pages = {1-40},
     zbl = {1008.11015},
     mrnumber = {1882023},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2001_4_30_1_1_0}
}

The arithmetic hyperbolic $3$-manifold of smallest volume. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 30 (2001) no. 1, pp. 1-40. http://www.numdam.org/item/ASNSP_2001_4_30_1_1_0/

[Ad] C. Adams, The noncompact hyperbolic 3-manifold of minimal volume, Proc. Amer. Math. Soc. 100 (1987), 601-606. | MR 894423 | Zbl 0634.57008

[At] M. Atria, Lower bounds for discriminants of octic number fields having six real places, Preprint (1996).

[BMO] A.M. Bergé - J. Martinet - M. Olivier, The computation of sextic fields with a quadratic subfield, Math. Comp. 54 (1990), 869-884. | MR 1011438 | Zbl 0709.11056

[Bo] A. Borel, 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] T. Chinburg, A small arithmetic hyperbolic 3-manifold, Proc. Amer. Math. Soc. 100 (1987), 140-144. | MR 883417 | Zbl 0621.57006

[CF1] T. Chinburg - E. Friedman, The smallest arithmetic hyperbolic three-orbifold, Invent. Math. 86 (1986), 507-527. | MR 860679 | Zbl 0643.57011

[CF2] T. Chinburg - E. Friedman, 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] T. Chinburg - E. Friedman, An embedding theorem for quaternion algebras, J. London Math. Soc. (2) 60 (1999), 33-44. | MR 1721813 | Zbl 0940.11053

[CF4] T. Chinburg - E. Friedman, Hilbert symbols, class groups and quaternion algebras, J. Théorie Nombres Bordeaux 12 (2000), 367-377. | Numdam | MR 1823190 | Zbl 0973.11097

[Co] H. Cohen et al., PARI, Freeware available by anonymous FTP from megrez.math.u-bordeaux.fr, directory pub/pari.

[Cu] M. Culler, Lifting representations to covering groups, Adv. Math. 59 (1986), 64-70. | MR 825087 | Zbl 0582.57001

[CS1] M. Culler - P.B. Shalen, 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] M. Culler - P.B. Shalen, Volumes of Haken manifolds, I, Invent. Math. 118 (1994), 285-329. | MR 1292114 | Zbl 0862.57008

[CS3] M. Culler - P.B. Shalen, Varieties of group representations and splittings of 3-manifolds, Ann. of Math. 117 (1983), 109-146. | MR 683804 | Zbl 0529.57005

[CHS] M. Culler - S. Hersonsky - P.B. Shalen, The first betti number of the smallest closed hyperbolic 3-manifold, Topology 37 (1998), 805-849. | MR 1607748 | Zbl 0893.57015

[EEK] A.L. Edmonds - J.H. Ewing - R.S. Kulkarni, Torsion free subgroups of Fuchsian groups and tessellations of surfaces, Invent. Math. 69 (1982), 331-346. | MR 679761 | Zbl 0498.20033

[GMT] D. Gabai - G.R. Meyerhoff - N. Thurston, Homotopy hyperbolic 3-manifolds are hyperbolic, To appear Ann. of Math. | MR 1973051 | Zbl 1052.57019

[GMMR] F.W. Gehring - C. Maclachlan - G.J. Martin - A.W. Reid, Arithmeticity, discreteness and volume, Trans. Amer. Math. Soc. 349 (1997), 3611-3643. | MR 1433117 | Zbl 0889.30031

[GM] F.W. Gehring - G.J. Martin, Precisely invariant collars and the volume of hyperbolic 3-folds, J. Differential Geom. 49 (1998), 411-435. | MR 1669657 | Zbl 0989.57010

[Gr] M. Gromov, "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] C.D. Hodgson - J. Weeks, Symmetries, isometries, and length spectra of closed hyperbolic 3-manifolds, Experimental Math. 3 (1994), 101-113. | MR 1341719 | Zbl 0841.57020

[JRI] K.N. Jones - A.W. Reid, Minimal index torsion-free subgroups of Kleinian groups, Math. Ann. 310 (1998), 235-250. | MR 1602004 | Zbl 0890.57016

[JR2] K.N. Jones - A.W. Reid, Computational methods in arithmetic Kleinian groups, in preparation.

[MR1] C. Maclachlan - A.W. Reid, 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] C. Maclachlan - A.W. Reid, "The Arithmetic of Hyperbolic 3-Manifolds ", To appear Springer Verlag. | MR 1937957 | Zbl 1025.57001

[Ma] J. Martinet, 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] A. Mednykh - A. Vesnin, 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] G.D. Mostow, 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] M. Olivier, Corps sextiques primitifs, Ann. Inst. Fourier (Grenoble) 40 (1990), 757-767. | Numdam | MR 1096589 | Zbl 0734.11054

[O2] M. Olivier, 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] G. Poitou, 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] G. Prasad, Q-rank one lattices, Invent. Math. 21 (1973), 255-286. | MR 385005 | Zbl 0264.22009

[Prz] A. Przeworski, Cones embedded in hyperbolic 3-manifolds, Preprint (2000).

[RW] A.W. Reid - S. Wang, 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] W. Thurston, "The Geometry and Topology of 3-Manifolds", Mimeographed Lecture Notes, Princeton Univ., 1977.

[Vi] M.-F. Vignéras, "Arithmétique des algèbres de Quaternions", L.N.M. 800, Springer Verlag, Berlin, 1980. | MR 580949 | Zbl 0422.12008

[We1] J. Weeks, "Hyperbolic Structures on 3-manifolds", Ph. D. Thesis, Princeton University, 1985.

[We2] J. Weeks, SnapPea: A computer program for creating and studying hyperbolic 3- manifolds, available by anonymous ftp from www.northnet.org/weeks/.