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On the Mal'cev quotients of certain hyperbolic link groups

Published online by Cambridge University Press:  24 October 2008

S. P. Humphries  and
D. D. Long
S. P. Humphries
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A.
D. D. Long
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A.
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Extract

In the understanding of hyperbolic 3-manifolds, some of the important open questions revolve around the behaviour of a surface upon the passage to a finite covering space; for example one would like to know if it is possible to replace an immersion by an embedding, or a separating surface by a non-separating one.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 3 , November 1987 , pp. 475 - 480
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCES

[1]Grunewald, F. J. and Schwermer, J.. Arithmetic quotients of hyperbolic 3-space, cusp forms and link complements. Duke Math. J. 8 (1981), 351–358.Google Scholar
[2]Hartley, B. and Hawkes, T.. Rings, modules and linear algebra (Chapman and Hall, 1970).Google Scholar
[3]Hatcher, A.. Hyperbolic structures of arithmetic type on some link complements. J. London Math. Soc. (2) 27 (1983), 345–355.CrossRefGoogle Scholar
[4]Long, D. D.. Engulfing and subgroup separability for hyperbolic groups. Trans. Amer. Math. Soc., to appear.Google Scholar
[5]Lubotzky, A.. Group presentation, p-adic analytic groups and lattices in SL 2(ℂ). Ann. of Math. 118 (1983), 115–130.CrossRefGoogle Scholar
[6]Margulis, G. and Soifer, G.. Maximal subgroups of infinite index in infinitely generated linear groups. J. Algebra 69 (1981), 1–23.CrossRefGoogle Scholar
[7]Riley, R.. A quadratic parabolic group. Math. Proc. Cambridge Philos. Soc. 77 (1975), 218–288.CrossRefGoogle Scholar
[8]Scott, G. P.. Subgroups of surface groups are almost geometric. J. London Math. Soc. 17 (1978), 555–565.CrossRefGoogle Scholar
[9]Schwermer, J. and Vogtmann, K.. The integral homology of SL 2 and PSL 2 of euclidean imaginary quadratic integers. Comment. Math. Helv. 58 (1983), 573–598.CrossRefGoogle Scholar
[10]Serre, J.-P.. Le problème des groupes de congruence pour SL 2. Ann. of Math. 92 (1970), 489–527.Google Scholar
[11]Thurston, W. P.. The geometry and topology of 3-manifolds. Princeton Lecture Notes.Google Scholar
[12]Wehrfritz, B. A. F.. Infinité linear groups (Springer-Verlag, 1973).Google Scholar