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arXiv · 1506.03839

Groups with infinitely many ends acting analytically on the circle

Sébastien Alvarez·Dmitry Filimonov·Victor Kleptsyn·Dominique Malicet·Carlos Meniño Cotón·Andrés Navas·Michele Triestino
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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.

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Sébastien Alvarez, Dmitry Filimonov, Victor Kleptsyn, Dominique Malicet, Carlos Meniño Cotón, Andrés Navas, Michele Triestino. 2015-06-11. Groups with infinitely many ends acting analytically on the circle. https://doi.org/10.1112/topo.12118

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