Concentration points for Fuchsian groups

Sungbok Hong, Dairyl McCullough

Research output: Contribution to journalArticle

Abstract

A limit point p of a discrete group of Möbius 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, for finitely generated Fuchsian groups. In the infinitely generated case, it implies that 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.

Original languageEnglish
Pages (from-to)285-303
Number of pages19
JournalTopology and its Applications
Volume105
Issue number3
Publication statusPublished - 2000 Dec 1

    Fingerprint

Keywords

  • Concentration
  • Concentration point
  • Conical limit point
  • Controlled
  • Fuchsian group
  • Geodesic lamination
  • Geodesic separation point
  • Kleinian group
  • Lamination
  • Limit point
  • Möbius group
  • Point of approximation
  • Schottky group
  • Weak

ASJC Scopus subject areas

  • Geometry and Topology

Cite this