# zbMATH — the first resource for mathematics

Intersections of analytically and geometrically finite subgroups of Kleinian groups. (English) Zbl 0802.30036
For a pair $$(G,J)$$ of subgroups of a Kleinian group of the second kind, where $$G$$ is analytically finite, and $$J$$ is geometrically finite, possibly infinite cyclic, their intersection is investigated. The cases when $$J$$ is infinite cyclic, and $$J$$ is nonelementary are studied. In both cases the limit set of the intersection is equal to the intersection of the limit sets.

##### MSC:
 30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
Kleinian group
Full Text:
##### References:
 [1] James W. Anderson, Intersections of topologically tame subgroups of Kleinian groups, J. Anal. Math. 65 (1995), 77 – 94. · Zbl 0832.30027 · doi:10.1007/BF02788766 · doi.org [2] James W. Anderson, On the finitely generated intersection property for Kleinian groups, Complex Variables Theory Appl. 17 (1991), no. 1-2, 111 – 112. · Zbl 0724.30036 [3] Alan F. Beardon and Bernard Maskit, Limit points of Kleinian groups and finite sided fundamental polyhedra, Acta Math. 132 (1974), 1 – 12. · Zbl 0277.30017 · doi:10.1007/BF02392106 · doi.org [4] A. F. Beardon and Ch. Pommerenke, The Poincaré metric of plane domains, J. London Math. Soc. (2) 18 (1978), no. 3, 475 – 483. · Zbl 0399.30008 · doi:10.1112/jlms/s2-18.3.475 · doi.org [5] Richard D. Canary, Covering theorems for hyperbolic 3-manifolds, Low-dimensional topology (Knoxville, TN, 1992) Conf. Proc. Lecture Notes Geom. Topology, III, Int. Press, Cambridge, MA, 1994, pp. 21 – 30. · Zbl 0849.57014 [6] Richard D. Canary, The Poincaré metric and a conformal version of a theorem of Thurston, Duke Math. J. 64 (1991), no. 2, 349 – 359. · Zbl 0759.57013 · doi:10.1215/S0012-7094-91-06417-3 · doi.org [7] John Hempel, The finitely generated intersection property for Kleinian groups, Knot theory and manifolds (Vancouver, B.C., 1983) Lecture Notes in Math., vol. 1144, Springer, Berlin, 1985, pp. 18 – 24. · doi:10.1007/BFb0075010 · doi.org [8] Irwin Kra, Automorphic forms and Kleinian groups, W. A. Benjamin, Inc., Reading, Mass., 1972. Mathematics Lecture Note Series. · Zbl 0253.30015 [9] Bernard Maskit, Intersections of component subgroups of Kleinian groups, Discontinuous groups and Riemann surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973) Princeton Univ. Press, Princeton, N.J., 1974, pp. 349 – 367. Ann. of Math. Studies, No. 79. [10] Bernard Maskit, Kleinian groups, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 287, Springer-Verlag, Berlin, 1988. · Zbl 0627.30039 [11] John W. Morgan, On Thurston’s uniformization theorem for three-dimensional manifolds, The Smith conjecture (New York, 1979) Pure Appl. Math., vol. 112, Academic Press, Orlando, FL, 1984, pp. 37 – 125. · doi:10.1016/S0079-8169(08)61637-2 · doi.org [12] Teruhiko Soma, Function groups in Kleinian groups, Math. Ann. 292 (1992), no. 1, 181 – 190. · Zbl 0739.30033 · doi:10.1007/BF01444616 · doi.org [13] Perry Susskind, Kleinian groups with intersecting limit sets, J. Analyse Math. 52 (1989), 26 – 38. · Zbl 0677.30028 · doi:10.1007/BF02820470 · doi.org [14] Perry Susskind and Gadde A. Swarup, Limit sets of geometrically finite hyperbolic groups, Amer. J. Math. 114 (1992), no. 2, 233 – 250. · Zbl 0791.30039 · doi:10.2307/2374703 · doi.org
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.