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Structure theorems for subgroups of homeomorphism groups

Structure theorems for subgroups of homeomorphism groups
Structure theorems for subgroups of homeomorphism groups
Let Homeo(S1) represent the full group of homeomorphisms of the unit circle S1, and let A represent the set of subgroups of Homeo(S1) satisfying the two properties that if G ? A then 1) G contains only orientation preserving homeomorphisms of S1 and 2) G contains no non-abelian free subgroups. This expository article uses classical results about homeomorphisms of the circle and elementary dynamical methods to derive various new and old results about the groups in A; we give a general structure theorem for such groups within a family of such results by Beklaryan, Malyutin, and Solodov, a new proof of Margulis’ Theorem that given G ? A the circle S1 admits a G-invariant probability measure, and we classify the solvable subgroups of R. Thompson’s group T.
Bleak, Collin
88ded533-1f6e-4286-93e5-a724536076be
Kassabov, Martin
b78efbac-c468-4838-ac56-5f23181f595c
Matucci, Francesco
b4661e9d-c6e3-41b6-b545-400b77afc190
Bleak, Collin
88ded533-1f6e-4286-93e5-a724536076be
Kassabov, Martin
b78efbac-c468-4838-ac56-5f23181f595c
Matucci, Francesco
b4661e9d-c6e3-41b6-b545-400b77afc190

Bleak, Collin, Kassabov, Martin and Matucci, Francesco (2010) Structure theorems for subgroups of homeomorphism groups. Pre-print.

Record type: Article

Abstract

Let Homeo(S1) represent the full group of homeomorphisms of the unit circle S1, and let A represent the set of subgroups of Homeo(S1) satisfying the two properties that if G ? A then 1) G contains only orientation preserving homeomorphisms of S1 and 2) G contains no non-abelian free subgroups. This expository article uses classical results about homeomorphisms of the circle and elementary dynamical methods to derive various new and old results about the groups in A; we give a general structure theorem for such groups within a family of such results by Beklaryan, Malyutin, and Solodov, a new proof of Margulis’ Theorem that given G ? A the circle S1 admits a G-invariant probability measure, and we classify the solvable subgroups of R. Thompson’s group T.

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Structure_Theorems_for_Subgroups_of_Homeomorphism_Groups.pdf - Author's Original
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Published date: November 2010

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Local EPrints ID: 155199
URI: https://eprints.soton.ac.uk/id/eprint/155199
PURE UUID: 34a85969-d2c0-4944-a4f2-54e1362ed874

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Date deposited: 28 May 2010 10:53
Last modified: 18 Jul 2017 12:45

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