Duke Mathematical Journal

Geodesic intersections in arithmetic hyperbolic $3$-manifolds

Kerry N. Jones and Alan W. Reid
Source: Duke Math. J. Volume 89, Number 1 (1997), 75-86.
First Page: Show Hide
Primary Subjects: 57M50
Secondary Subjects: 20H10, 57N10
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077240834
Mathematical Reviews number (MathSciNet): MR1458971
Zentralblatt MATH identifier: 0887.57015
Digital Object Identifier: doi:10.1215/S0012-7094-97-08904-3

References

[BW] A. Basmajian and S. Wolpert, Hyperbolic $3$-manifolds with no self-intersecting closed geodesics, in preparation.
[B] H. Bass, Groups of integral representation type, Pacific J. Math. 86 (1980), no. 1, 15–51.
Mathematical Reviews (MathSciNet): MR82c:20014
Zentralblatt MATH: 0444.20006
Project Euclid: euclid.pjm/1102780613
[Bo] A. Borel, Commensurability classes and volumes of hyperbolic $3$-manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 8 (1981), no. 1, 1–33.
Mathematical Reviews (MathSciNet): MR82j:22008
Zentralblatt MATH: 0473.57003
[CR] T. Chinburg and A. W. Reid, Closed hyperbolic $3$-manifolds whose closed geodesics all are simple, J. Differential Geom. 38 (1993), no. 3, 545–558.
Mathematical Reviews (MathSciNet): MR94k:57020
Zentralblatt MATH: 0783.53028
Project Euclid: euclid.jdg/1214454482
[GMMR] F. W. Gehring, C. Maclachlan, G. J. Martin, and A. W. Reid, Arithmeticity, discreteness and volume, to appear in Trans. Amer. Math. Soc.
Mathematical Reviews (MathSciNet): MR1433117
Zentralblatt MATH: 0889.30031
Digital Object Identifier: doi:10.1090/S0002-9947-97-01989-2
[HLM] H. M. Hilden, M.-T. Lozano, and J.-M. Montesinos, A characterization of arithmetic subgroups of $\rm SL(2,\bf R)$ and $\rm SL(2,\bf C)$, Math. Nachr. 159 (1992), 245–270.
Mathematical Reviews (MathSciNet): MR94i:20088
Zentralblatt MATH: 0786.20031
Digital Object Identifier: doi:10.1002/mana.19921590117
[JR] K. N. Jones and A. W. Reid, Non-simple geodesics in hyperbolic $3$-manifolds, Math. Proc. Cambridge Philos. Soc. 116 (1994), no. 2, 339–351.
Mathematical Reviews (MathSciNet): MR95e:57025
Zentralblatt MATH: 0865.57017
Digital Object Identifier: doi:10.1017/S0305004100072625
[La] S. Lang, Algebraic number theory, Graduate Texts in Mathematics, vol. 110, Springer-Verlag, New York, 1994.
Mathematical Reviews (MathSciNet): MR95f:11085
Zentralblatt MATH: 0811.11001
[MR] C. Maclachlan and A. W. Reid, Commensurability classes of arithmetic Kleinian groups and their Fuchsian subgroups, Math. Proc. Cambridge Philos. Soc. 102 (1987), no. 2, 251–257.
Mathematical Reviews (MathSciNet): MR88j:20040
Zentralblatt MATH: 0632.30043
Digital Object Identifier: doi:10.1017/S030500410006727X
[Mar] G. Margulis, Discrete subgroups of semisimple Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 17, Springer-Verlag, Berlin, 1991.
Mathematical Reviews (MathSciNet): MR92h:22021
Zentralblatt MATH: 0732.22008
[NR] W. D. Neumann and A. W. Reid, Arithmetic of hyperbolic manifolds, Topology '90 (Columbus, OH, 1990), Ohio State Univ. Math. Res. Inst. Publ., vol. 1, de Gruyter, Berlin, 1992, pp. 273–310.
Mathematical Reviews (MathSciNet): MR94c:57024
Zentralblatt MATH: 0777.57007
[O] O. T. O'Meara, Introduction to quadratic forms, Die Grundlehren der mathematischen Wissenschaften, Bd. 117, Academic Press Inc., Publishers, New York, 1963.
Mathematical Reviews (MathSciNet): MR27:2485
Zentralblatt MATH: 0107.03301
[R] A. W. Reid, A note on trace-fields of Kleinian groups, Bull. London Math. Soc. 22 (1990), no. 4, 349–352.
Mathematical Reviews (MathSciNet): MR91d:20056
Zentralblatt MATH: 0706.20038
Digital Object Identifier: doi:10.1112/blms/22.4.349
[R2] A. W. Reid, Isospectrality and commensurability of arithmetic hyperbolic $2$- and $3$-manifolds, Duke Math. J. 65 (1992), no. 2, 215–228.
Mathematical Reviews (MathSciNet): MR93b:58158
Zentralblatt MATH: 0776.58040
Digital Object Identifier: doi:10.1215/S0012-7094-92-06508-2
Project Euclid: euclid.dmj/1077295133
[Ri] R. Riley, Parabolic representations and symmetries of the knot $9\sb 32$, Computers in geometry and topology (Chicago, IL, 1986) ed. M. C. Tangora, Lecture Notes in Pure and Appl. Math., vol. 114, Dekker, New York, 1989, pp. 297–313.
Mathematical Reviews (MathSciNet): MR90d:57008
Zentralblatt MATH: 0677.57008
[Ro] D. Rolfsen, Knots and links, Publish or Perish Inc., Berkeley, Calif., 1976.
Mathematical Reviews (MathSciNet): MR58:24236
Zentralblatt MATH: 0339.55004
[T] W. P. Thurston, The geometry and topology of three-manifolds, mimeographed lecture notes, Princeton Univ., Princeton, 1997.
Mathematical Reviews (MathSciNet): MR1435975
Zentralblatt MATH: 0873.57001
[V] M.-F. Vignéras, Arithmétique des algèbres de quaternions, Lecture Notes in Mathematics, vol. 800, Springer, Berlin, 1980.
Mathematical Reviews (MathSciNet): MR82i:12016
Zentralblatt MATH: 0422.12008

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