Classification of continuously transitive circle groups
| dc.creator | Giblin, James | |
| dc.creator | Markovic, Vladimir | |
| dc.date | 2009-03-01 | |
| dc.date.accessioned | 2026-07-07T12:48:03Z | |
| dc.date.available | 2026-07-07T12:48:03Z | |
| dc.description | Let G be a closed transitive subgroup of Homeo(S^1) which contains a non-constant continuous path f: [0,1] --> G. We show that up to conjugation G is one of the following groups: SO(2,R), PSL(2,R), PSL_k(2,R), Homeo_k(S^1), Homeo(S^1). This verifies the classification suggested by Ghys [Enseign. Math. 47 (2001) 329-407]. As a corollary we show that the group PSL(2,R) is a maximal closed subgroup of Homeo(S^1) (we understand this is a conjecture of de la Harpe). We also show that if such a group G < Homeo(S^1) acts continuously transitively on k-tuples of points, k>3, then the closure of G is Homeo(S^1) (cf Bestvina's collection of `Questions in geometric group theory'). | |
| dc.description | This is the version published by Geometry & Topology on 18 September 2006 | |
| dc.identifier | https://arxiv.org/abs/0903.0180 | |
| dc.identifier | http://arxiv.org/abs/0903.0180 | |
| dc.identifier | Geom. Topol. 10 (2006) 1319-1346 | |
| dc.identifier | doi:10.2140/gt.2006.10.1319 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221925 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 37E10, 22A05, 54H11 | |
| dc.title | Classification of continuously transitive circle groups | |
| dc.type | text |