Classification of continuously transitive circle groups
Giblin, James and Markovic, Vladimir. (2006) Classification of continuously transitive circle groups. GEOMETRY & TOPOLOGY, 10 . pp. 1319-1346. ISSN 1364-0380Full text not available from this repository.
Official URL: http://dx.doi.org/10.2140/gt.2006.10.1319
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 . 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 ).
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||GEOMETRY & TOPOLOGY|
|Publisher:||GEOMETRY & TOPOLOGY PUBLICATIONS|
|Number of Pages:||28|
|Page Range:||pp. 1319-1346|
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