Weak concentration points for Möbius groups.

*(English)*Zbl 0805.20041A limit point \(p \in \partial D^ m\) of a discrete group of Möbius transformations acting on \(D^ m\) is called a weak concentration point if there exists a connected open set in \(\partial D^ m\) whose set of translates contains a local basis for the topology at \(p\). Every conical limit point is a weak concentration point. When \(m = 2\), a complete characterization is obtained. In all dimensions, a sufficient condition for \(p\) to be a weak concentration point is given. It shows that every parabolic fixed point is a weak concentration point, and consequently all limit points of geometrically finite groups are weak concentration points. Moreover, it shows that whenever the limit set is all of \(\partial D^ m\), every limit point is a weak concentration point, and that for any group all but countably many points of the limit set are weak concentration points.

Reviewer: D.McCullough (Norman)

##### MSC:

20H10 | Fuchsian groups and their generalizations (group-theoretic aspects) |

30F35 | Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) |

30F40 | Kleinian groups (aspects of compact Riemann surfaces and uniformization) |

57M99 | General low-dimensional topology |