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Link complements and the Bianchi modular groups


Author: Mark D. Baker
Journal: Trans. Amer. Math. Soc. 353 (2001), 3229-3246
MSC (2000): Primary 57M25; Secondary 11F06
DOI: https://doi.org/10.1090/S0002-9947-01-02555-7
Published electronically: April 9, 2001
MathSciNet review: 1695016
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Abstract: We determine the values of $m$ for which the Bianchi modular group $\operatorname{PSL}_2(\mathcal{O}_m)$ contains a link group.


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  • [B] M. Baker, Link complements and integer rings of class number greater than one, Topology `90 (Proceedings of the research semester in Low Dimensional Topology at Ohio State University), Walter de Gruyter, Berlin, New York (1992), 55-59. MR 93k:57007
  • [G] GAP (Groups, algorithms, and programming). Available from: http://www.gap.dcs.st-and.ac.uk/~gap/.
  • [H1] A. Hatcher, Hyperbolic structures of arithmetic type on some link complements, J. London Math. Soc. (2), 27 (1983), 345-355. MR 84m:57005
  • [H2] A Hatcher, Bianchi orbifolds of small discriminant, preprint (available from author's web page).
  • [P] Pari, Available from Université de Bordeaux: http://www.math.u-bordeaux.fr/A2X.
  • [R1] R. Riley, A quadratic parabolic group, Math. Proc. Cambridge Philos. Soc. 77 (1975), 281-288. MR 54:542
  • [R2] R. Riley, Applications of a computer implementation of Poincaré's theorem on fundamental polyhedra, Math. Comp. 40 (1983), 607-632. MR 85b:20064
  • [Ro] D. Rolfsen, Knots and Links, Publish or Perish, Inc., Berkeley, (1976). MR 58:24236; corrected reprint MR 95c:57018
  • [S] J.-P. Serre, Le problème des groupes de congruence pour $\operatorname{SL}_2$, Ann. of Math. 92 (1972), 489-527. MR 42:7671
  • [Sw] R. Swan, Generators and relations for certain special linear groups, Adv. in Math. 6 (1971), 1-77. MR 44:1741
  • [T] W. Thurston, The geometry and topology of $3$-manifolds, Mimeographed notes, Princeton University, 1978.
  • [V] K. Vogtmann, Rational homology of Bianchi groups, Math. Ann. 272 (1985), 399-419. MR 87a:22025
  • [W] J. Weeks, SnapPea 2.4 PPC. Available from: weeks@geom.umn.edu.
  • [Wi] N. Wielenberg, The structure of certain subgroups of the Picard group, Math. Proc. Cambridge Philos. Soc. 84 (1978), 427-436. MR 80b:57010

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Additional Information

Mark D. Baker
Affiliation: IRMAR, Université de Rennes 1, 35042 Rennes cedex, France

DOI: https://doi.org/10.1090/S0002-9947-01-02555-7
Keywords: Link complements, Bianchi modular groups
Received by editor(s): June 3, 1998
Received by editor(s) in revised form: March 8, 1999
Published electronically: April 9, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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