Geometric finiteness of certain Kleinian groups
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- by G. P. Scott and G. A. Swarup
- Proc. Amer. Math. Soc. 109 (1990), 765-768
- DOI: https://doi.org/10.1090/S0002-9939-1990-1013981-6
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Abstract:
If $G$ is a discrete subgroup of $\operatorname {PSL} \left ( {2;{\mathbf {C}}} \right )$ representing a fibred $3$-manifold and $H$ the subgroup of $G$ corresponding to the fibre, we show that any finitely generated subgroup of infinite index in $H$ is geometrically finite.References
- Francis Bonahon, Bouts des variétés hyperboliques de dimension $3$, Ann. of Math. (2) 124 (1986), no. 1, 71–158 (French). MR 847953, DOI 10.2307/1971388
- James W. Cannon and William P. Thurston, Group invariant Peano curves, Geom. Topol. 11 (2007), 1315–1355. MR 2326947, DOI 10.2140/gt.2007.11.1315 S. Fenley, Ph.D. thesis, Princeton, 1989.
- Leon Greenberg, Discrete groups of motions, Canadian J. Math. 12 (1960), 415–426. MR 115130, DOI 10.4153/CJM-1960-036-8
- Bernard Maskit, On free Kleinian groups, Duke Math. J. 48 (1981), no. 4, 755–765. MR 782575, DOI 10.1215/S0012-7094-81-04841-9
- Peter Scott, Subgroups of surface groups are almost geometric, J. London Math. Soc. (2) 17 (1978), no. 3, 555–565. MR 494062, DOI 10.1112/jlms/s2-17.3.555
- Peter Scott, Correction to: “Subgroups of surface groups are almost geometric” [J. London Math. Soc. (2) 17 (1978), no. 3, 555–565; MR0494062 (58 #12996)], J. London Math. Soc. (2) 32 (1985), no. 2, 217–220. MR 811778, DOI 10.1112/jlms/s2-32.2.217 W. Thurston, Hyperbolic structures on $3$-manifolds II, Surface groups and $3$-manifolds which fibre over the circle, preprint, 1987. —, Notes on hyperbolic geometry, Princeton, NJ, preprint.
Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 765-768
- MSC: Primary 57M05; Secondary 57N10
- DOI: https://doi.org/10.1090/S0002-9939-1990-1013981-6
- MathSciNet review: 1013981