Groups With Infinitely Many Ends Acting Analytically On The Circle

This article is inspired by two milestones in the study of non-minimal group actions on the circle: Duminy’s theorem about the number of ends of semi-exceptional leaves, and Ghys’ freeness result in real-analytic regularity. Our first result concerns groups of real-analytic diffeomorphisms with infinitely many ends: if the action is non-expanding, then the group is virtually free. The second result is a Duminy type theorem for minimal codimension-one foliations: either non-expandable leaves have infinitely many ends, or the holonomy pseudogroup preserves a projective structure.