Concentration points for Fuchsian groups

Details Concentration points for Fuchsian groups Concentration points for Fuchsian groups

1998-06-23

arxiv.org/abs/math/9806122v1

Mathematics

Geometric Topology

24 pages, 7 figures

Scientific paper

A limit point p of a discrete group of Mobius transformations acting on S^n is called a concentration point if for any sufficiently small connected open neighborhood U of p, the set of translates of U contains a local basis for the topology of S^n at p. For the case of Fuchsian groups (n = 1), every concentration point is a conical limit point, but even for finitely generated groups not every conical limit point is a concentration point. A slightly weaker concentration condition is given which is satisfied if and only if p is a conical limit point, but not all conical limit points satisfy it. Examples are given that clarify the relations between various concentration conditions.

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