Volume 10, issue 3 (2006)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 27
Issue 9, 3387–3831
Issue 8, 2937–3385
Issue 7, 2497–2936
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Classification of continuously transitive circle groups

James Giblin and Vladimir Markovic

Geometry & Topology 10 (2006) 1319–1346

arXiv: 0903.0180

Abstract

Let G be a closed transitive subgroup of Homeo(S1) 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, ), PSL(2, ), PSLk(2, ), Homeok(S1), Homeo(S1). This verifies the classification suggested by Ghys in [Enseign. Math. 47 (2001) 329-407]. As a corollary we show that the group PSL(2, ) is a maximal closed subgroup of Homeo(S1) (we understand this is a conjecture of de la Harpe). We also show that if such a group G < Homeo(S1) acts continuously transitively on k–tuples of points, k > 3, then the closure of G is Homeo(S1) (cf Bestvina’s collection of ‘Questions in geometric group theory’).

Keywords
Circle group, convergence group, transitive group, cyclic cover
Mathematical Subject Classification 2000
Primary: 37E10
Secondary: 22A05, 54H11
References
Forward citations
Publication
Received: 12 December 2005
Revised: 22 June 2006
Accepted: 29 July 2006
Published: 18 September 2006
Proposed: David Gabai
Seconded: Leonid Polterovich, Benson Farb
Authors
James Giblin
Mathematics Institute
University of Warwick
Coventry, CV4 7AL
UK
http://www.maths.warwick.ac.uk/~giblin/
Vladimir Markovic
Mathematics Institute
University of Warwick
Coventry, CV4 7AL
UK
http://www.maths.warwick.ac.uk/~markovic/