English

The structure of extended function groups

Complex Variables 2021-07-08 v3 Geometric Topology

Abstract

A function group is a finitely generated Kleinian group with an invariant connected component of its region of discontinuity. An extended function group is a finitely generated extended Kleinian group that contains orientation reversing elements and keep invariant a connected components of its region of discontinuity. An structural decomposition of function groups, in terms of the Klein-Maskit combination theorems, was provided by Maskit in the middle of the 70's. One should expect a similar decomposition structure for extended function groups, but it seems not to be stated in the existing literature. The aim of this paper is to state and procvide a proof of such a decomposition structural picture.

Keywords

Cite

@article{arxiv.1812.06048,
  title  = {The structure of extended function groups},
  author = {Ruben A. Hidalgo},
  journal= {arXiv preprint arXiv:1812.06048},
  year   = {2021}
}
R2 v1 2026-06-23T06:42:52.149Z