## The nest subgroups of Kleinian groups

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- by Takehiko Sasaki PDF
- Trans. Amer. Math. Soc.
**278**(1983), 389-399 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

## Additional Information

- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**278**(1983), 389-399 - MSC: Primary 30F40
- DOI: https://doi.org/10.1090/S0002-9947-1983-0697083-5
- MathSciNet review: 697083