The nest subgroups of Kleinian groups

Sasaki, Takehiko

doi:10.1090/S0002-9947-1983-0697083-5

The nest subgroups of Kleinian groups
HTML articles powered by AMS MathViewer

by Takehiko Sasaki

Trans. Amer. Math. Soc. 278 (1983), 389-399

DOI: https://doi.org/10.1090/S0002-9947-1983-0697083-5

PDF | Request permission

Abstract:

The residual limit points of finitely generated Kleinian groups are classified into two types: the first kind and the second kind. To each point of the second kind, Abikoff associated a web subgroup. We shall classify the points of the first kind into two types and associate to each point of one type a finitely generated subgroup, the nest subgroup. To the points of the other type we shall give a significance showing that they are important for the sets of generators.

References

William Abikoff, The residual limit sets of Kleinian groups, Acta Math. 130 (1973), 127–144. MR 404613, DOI 10.1007/BF02392264
William Abikoff and Bernard Maskit, Geometric decompositions of Kleinian groups, Amer. J. Math. 99 (1977), no. 4, 687–697. MR 480992, DOI 10.2307/2373860
Tadashi Kuroda, Seiki Mori, and Hidenori Takahashi, Remarks on web groups, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978) Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 367–375. MR 624826
Bernard Maskit, Intersections of component subgroups of Kleinian groups, Discontinuous groups and Riemann surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973) Ann. of Math. Studies, No. 79, Princeton Univ. Press, Princeton, N.J., 1974, pp. 349–367. MR 0355037
Takehiko Sasaki, On common boundary points of more than two components of a finitely generated Kleinian group, Tôhoku Math. J. 29 (1977), no. 3, 427–437. MR 460627, DOI 10.2748/tmj/1178240608
Takehiko Sasaki, The residual limit sets and the generators of finitely generated Kleinian groups, Osaka Math. J. 15 (1978), no. 2, 263–282. MR 492236
Takehiko Sasaki, The residual limit points of the first kind and the nest groups, Tohoku Math. J. (2) 32 (1980), no. 1, 35–48. MR 567829, DOI 10.2748/tmj/1178229680