Giblin, James and Markovic, Vladimir. (2006) Classification of continuously transitive circle groups. GEOMETRY & TOPOLOGY, 10 . pp. 1319-1346. ISSN 1364-0380

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Abstract

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), PSLk(2,R), Homeo(k)(S-1), Homeo(S-1). This verifies the classification suggested by Ghys in [5]. 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 [1]).

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	GEOMETRY & TOPOLOGY
Publisher:	GEOMETRY & TOPOLOGY PUBLICATIONS
ISSN:	1364-0380
Date:	2006
Volume:	10
Number of Pages:	28
Page Range:	pp. 1319-1346
Identification Number:	10.2140/gt.2006.10.1319
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/32563

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