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Classification of continuously transitive circle groups
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Giblin, James and Markovic, Vladimir (2006) Classification of continuously transitive circle groups. GEOMETRY & TOPOLOGY, 10 . pp. 1319-1346. doi:10.2140/gt.2006.10.1319 ISSN 1364-0380.
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Official URL: http://dx.doi.org/10.2140/gt.2006.10.1319
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 | ||||
| Official Date: | 2006 | ||||
| Dates: |
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| Volume: | 10 | ||||
| Number of Pages: | 28 | ||||
| Page Range: | pp. 1319-1346 | ||||
| DOI: | 10.2140/gt.2006.10.1319 | ||||
| Publication Status: | Published |
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