Published September 18, 2006
| Published + Submitted
Journal Article
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Classification of continuously transitive circle groups
- Creators
- Giblin, James
- Markovic, Vladimir
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), PSL_k(2,ℝ), Homeo_k(S^1), Homeo(S^1). This verifies the classification suggested by Ghys in [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 G3, then the closure of G is Homeo(S^1) (cf Bestvina's collection of 'Questions in geometric group theory')
Additional Information
© 2006 Mathematical Sciences Publishers. Received: 12 December 2005; Revised: 22 June 2006; Accepted: 29 July 2006; Published: 18 September 2006.Attached Files
Published - gt-v10-n3-p03-p.pdf
Submitted - 0903.0180.pdf
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Additional details
- Eprint ID
- 77260
- Resolver ID
- CaltechAUTHORS:20170508-130256247
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2017-05-09Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field