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arXiv · 1812.06048

The structure of extended function groups

Ruben A. Hidalgo
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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.

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Ruben A. Hidalgo. 2018-12-14. The structure of extended function groups. https://arxiv.org/abs/1812.06048

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