no. 1
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 
@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},
     year = {2001},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 30},
     number = {1},
     mrnumber = {1882023},
     zbl = {1008.11015},
     language = {en},
     url = {https://www.numdam.org/item/ASNSP_2001_4_30_1_1_0/}
}
TY  - JOUR
AU  - Chinburg, Ted
AU  - Friedman, Eduardo
AU  - Jones, Kerry N.
AU  - Reid, Alan W.
TI  - The arithmetic hyperbolic $3$-manifold of smallest volume
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2001
SP  - 1
EP  - 40
VL  - 30
IS  - 1
PB  - Scuola normale superiore
UR  - https://www.numdam.org/item/ASNSP_2001_4_30_1_1_0/
LA  - en
ID  - ASNSP_2001_4_30_1_1_0
ER  - 
%0 Journal Article
%A Chinburg, Ted
%A Friedman, Eduardo
%A Jones, Kerry N.
%A Reid, Alan W.
%T The arithmetic hyperbolic $3$-manifold of smallest volume
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2001
%P 1-40
%V 30
%N 1
%I Scuola normale superiore
%U https://www.numdam.org/item/ASNSP_2001_4_30_1_1_0/
%G en
%F 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. https://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. | Zbl | MR

[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. | Zbl | MR

[Bo] A. Borel, Commensurability classes and volumes of hyperbolic 3-manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 8 (1981), 1-33. | Zbl | MR | Numdam

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

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

[CF2] T. Chinburg - E. Friedman, Finite subgroups of maximal arithmetic subgroups of PGL(2, C), Ann. Inst. Fourier (Grenoble) 50 (2000), 1765-1798. | Zbl | MR | Numdam

[CF3] T. Chinburg - E. Friedman, An embedding theorem for quaternion algebras, J. London Math. Soc. (2) 60 (1999), 33-44. | Zbl | MR

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

[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. | Zbl | MR

[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. | Zbl | MR

[CS2] M. Culler - P.B. Shalen, Volumes of Haken manifolds, I, Invent. Math. 118 (1994), 285-329. | Zbl | MR

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

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

[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. | Zbl | MR

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

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

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

[Gr] M. Gromov, "Hyperbolic Manifolds According to Thurston and Jørgensen", Séminaire Bourbaki 546, L.N.M. 842, Springer Verlag, Berlin, 1981. | Zbl | MR | Numdam

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

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

[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. | Zbl | MR

[MR2] C. Maclachlan - A.W. Reid, "The Arithmetic of Hyperbolic 3-Manifolds ", To appear Springer Verlag. | Zbl | MR

[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. | Zbl | MR

[MV] A. Mednykh - A. Vesnin, Visualization of the isometry group action on the Fomenko Matveev Weeks manifold, J. Lie Theory 8 (1998), 51-66. | Zbl | MR

[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. | Zbl | MR | Numdam

[O1] M. Olivier, Corps sextiques primitifs, Ann. Inst. Fourier (Grenoble) 40 (1990), 757-767. | Zbl | MR | Numdam

[O2] M. Olivier, The computation of sextic fields with a cubic subfield and no quadratic subfield, Math. Comp. 58 (1992), 419-432. | Zbl | MR

[Po] G. Poitou, Sur les petits discriminants, Séminaire Delange-Pisot-Poitou, Exposé n° 6 Paris, (1976/ 77), 6-01-6-18. | Zbl | MR | Numdam

[Pr] G. Prasad, Q-rank one lattices, Invent. Math. 21 (1973), 255-286. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

[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/.