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 Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/19252

 Title: Two Theorems of Dye in the Almost Continuous Category Authors: Zhuravlev, Vladimir Advisor: del Junco, Andres Department: Mathematics Keywords: orbit equivalenceergodic theory Issue Date: 3-Mar-2010 Abstract: This thesis studies orbit equivalence in the almost continuous setting. Recently A. del Junco and A. Sahin obtained an almost continuous version of Dye’s theorem. They proved that any two ergodic measure-preserving homeomorphisms of Polish spaces are almost continuously orbit equivalent. One purpose of this thesis is to extend their result to all free actions of countable amenable groups. We also show that the cocycles associated with the constructed orbit equivalence are almost continuous. In the second part of the thesis we obtain an analogue of Dye’s reconstruction theorem for etale equivalence relations in the almost continuous setting. We introduce topological full groups of etale equivalence relations and show that if the topological full groups are isomorphic, then the equivalence relations are almost continuously orbit equivalent. URI: http://hdl.handle.net/1807/19252 Appears in Collections: DoctoralDepartment of Mathematics - Doctoral theses

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