1998/06/23 by Sungbok Hong, Hong, Sungbok, Darryl McCullough +1
Mathematics · #20H10 (primary) #57M50 (secondary) #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:20H10 #msc:57M50
paper · pdf · doi:10.48550/arxiv.math/9806122
24 pages, 7 figures
arxiv created 1998/06/23 · arxiv updated 2009/11/30
A limit point p of a discrete group of Mobius transformations acting on Sn 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 Sn 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.