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Limit sets of geometrically finite hyperbolic groups. (English) Zbl 0791.30039
In this paper the authors study the existing relationship between geometrically finite hyperbolic groups in dimension $$n$$ and their limit sets. Also they extend to dimension $$n$$ several results which had already been established for dimension 2 and 3. Thus they prove: Let $$H \subseteq G$$ be hyperbolic groups with $$H$$ nonelementary and geometrically finite. If the limit sets $$\Delta (H)$$ and $$\Delta (G)$$ are equal, then the index of $$H$$ in $$G$$ is finite. Also they know that the intersection of two geometrically finite subgroups of a hyperbolic group is geometrically finite. Some properties of limit sets of intersection of two subgroups of a hyperbolic group are also studied.

##### MSC:
 30F99 Riemann surfaces 57N10 Topology of general $$3$$-manifolds (MSC2010) 51M10 Hyperbolic and elliptic geometries (general) and generalizations
##### Keywords:
limit sets; hyperbolic group
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