Projections in Moduli Spaces of the Kleinian Groups

Hala Alaqad, Jianhua Gong, Gaven Martin

Research output: Contribution to journalArticlepeer-review

Abstract

A two-generator Kleinian group f,g can be naturally associated with a discrete group f,φ with the generator φ of order two and where f,φfφ-1=f,gfg-1⊂f,g,f,φ: f,gfg-1=2. This is useful in studying the geometry of the Kleinian groups since f,g will be discrete only if f,φ is, and the moduli space of groups f,φ is one complex dimension less. This gives a necessary condition in a simpler space to determine the discreteness of f,g. The dimension reduction here is realised by a projection of principal characters of the two-generator Kleinian groups. In applications, it is important to know that the image of the moduli space of Kleinian groups under this projection is closed and, among other results, we show how this follows from Jørgensen's results on algebraic convergence.

Original languageEnglish
Article number6311193
JournalAbstract and Applied Analysis
Volume2022
DOIs
Publication statusPublished - 2022

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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