Geometry & Topology
- Geom. Topol.
- Volume 10, Number 3 (2006), 1319-1346.
Classification of continuously transitive circle groups
Let be a closed transitive subgroup of which contains a non-constant continuous path . We show that up to conjugation is one of the following groups: , , , , . This verifies the classification suggested by Ghys in [Enseign. Math. 47 (2001) 329-407]. As a corollary we show that the group is a maximal closed subgroup of (we understand this is a conjecture of de la Harpe). We also show that if such a group acts continuously transitively on –tuples of points, , then the closure of is (cf Bestvina’s collection of ‘Questions in geometric group theory’).
Geom. Topol., Volume 10, Number 3 (2006), 1319-1346.
Received: 12 December 2005
Revised: 22 June 2006
Accepted: 29 July 2006
First available in Project Euclid: 20 December 2017
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Giblin, James; Markovic, Vladimir. Classification of continuously transitive circle groups. Geom. Topol. 10 (2006), no. 3, 1319--1346. doi:10.2140/gt.2006.10.1319. https://projecteuclid.org/euclid.gt/1513799768