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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, Sér. 4, 30 no. 1 (2001), p. 1-40
Full text djvu | pdf | Reviews MR 1882023 | Zbl 1008.11015 | 3 citations in Numdam

stable URL: http://www.numdam.org/item?id=ASNSP_2001_4_30_1_1_0

Bibliography

[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.
Article |  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/.
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