Groups with infinitely many ends acting analytically on the circle
Dynamical Systems
2019-07-03 v5 Group Theory
Abstract
This article takes the inspiration from two milestones in the study of non minimal actions of groups on the circle: Duminy's theorem about the number of ends of semi-exceptional leaves and Ghys' freeness result in analytic regularity. Our first result concerns groups of analytic diffeomorphisms with infinitely many ends: if the action is non expanding, then the group is virtually free. The second result is a Duminy's theorem for minimal codimension one foliations: either non expandable leaves have infinitely many ends, or the holonomy pseudogroup preserves a projective structure.
Cite
@article{arxiv.1506.03839,
title = {Groups with infinitely many ends acting analytically on the circle},
author = {Sébastien Alvarez and Dmitry Filimonov and Victor Kleptsyn and Dominique Malicet and Carlos Meniño Cotón and Andrés Navas and Michele Triestino},
journal= {arXiv preprint arXiv:1506.03839},
year = {2019}
}
Comments
We can now make a precise reference to Deroin's work arXiv:1811.10298. 54 pages, 2 figures