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.
Cite
@article{arxiv.1812.06048,
title = {The structure of extended function groups},
author = {Ruben A. Hidalgo},
journal= {arXiv preprint arXiv:1812.06048},
year = {2021}
}