Groups with infinitely many ends acting analytically on the circle. Issue 4 (24th June 2019)

• Record Type: Journal Article
• Authors: Alvarez, Sébastien; Filimonov, Dmitry; Kleptsyn, Victor; Malicet, Dominique; Meniño Cotón, Carlos; Navas, Andrés; Triestino, Michele
• Is Part Of: Journal of topology. Volume 12:Issue 4(2019)
• Page Start: 1315
• Page End: 1367
• Publication Date: 2019-06-24
• Subjects: 37C85 (primary) -- 20E06 -- 37D25 -- 37F15 -- 57S05 (secondary); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12118
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: 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.