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Amalgamation and the invariant trace field of a Kleinian group

  • Walter D. Neumann (a1) and Alan W. Reid (a1)

Let Γ be a Kleinian group of finite covolume and denote by Γ(2) the subgroup generated by {γ2:γ ∈ Γ}. In [9] the trace field of Γ(2) was shown to be an invariant of the commensurability class of Γ. In [8] this field was termed the invariant trace field of Γ and further properties of this field were studied. Following the notation of [8] we denote the invariant trace field of Γ by k(Γ).

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[1]Adams C.. Thrice punctured spheres in hyperbolic 3-manifolds. Trans. Amer. Math. Soc. 287 (1985), 645656.
[2]Faltings G.. Endlichkeitssätze für abelsche Varietäten über Zahlkörpern. Invent. Math. 73 (1983), 349366;
Invent. Math. 75 (1984), 381.
[3]Kerckhoff S. P.. The Neilsen Realization Problem. Ann. of Math. (2) 117 (1983), 235265.
[4]Lickorish W. B. R. and Millet K. C.. A polynomial invariant of oriented links. Topology 26 (1987), 107141.
[5]Macbeath A. M.. Commensurability of cocompact three-dimensional hyperbolic groups. Duke Math. J. 50 (1983), 12451253.
[6]Meyerhoff R. and Ruberman D.. Mutation and the η-invariant. J. Differential Geom. 31 (1990), 101130.
[7]Milnor J.. Singular Points of Complex Hypersurfaces. Annals of Math. Studies no. 61 (Princeton University Press, 1968).
[8]Neumann W. D. and Reid A. W.. Arithmetic of hyperbolic 3-manifolds. O.S.U. Math. Research Inst. Preprint 90–5 (1990) to appear in: TOPOLOGY '90, Proceedings of the Research Semester in Low Dimensional Topology at Ohio State Univ. (de Gruyter, Berlin, 1991).
[9]Reid A. W.. A note on trace-fields of Kleinian groups. Bull. London Math. Soc. 22 (1990), 349352.
[10]Ruberman D.. Mutations and volumes of links in S 3. Invent. Math. 90 (1987), 189215.
[11]Thistlethwaite M. B.. Knot tabulations and related topics. In Aspects of Topology (editors, James I. M. and Kronheimer E. H.), London Math. Soc. Lecture Note Ser. Ca. 93 (Cambridge University Press, 1985), pp. 176.
[12]Thurston W. P.. The Geometry and Topology of 3-Manifolds. Mimeographed lecture notes (Princeton University, 1977).
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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