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Isomorphism of Borel full groups |
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| Authors: | Benjamin D. Miller Christian Rosendal |
| Affiliation: | Department of Mathematics, University of California Los Angeles, Box 951555, Los Angeles, California 90095-1555 ; Department of Mathematics 253-37, California Institute of Technology, Pasadena, California 91125 |
| Abstract: | Suppose that  and  are Polish groups which act in a Borel fashion on Polish spaces  and  . Let  and  denote the corresponding orbit equivalence relations, and ![$ [G]$](http://www.ams.org/proc/2007-135-02/S0002-9939-06-08542-X/gif-abstract0/img7.gif){kind=small} and ![$ [H]$](http://www.ams.org/proc/2007-135-02/S0002-9939-06-08542-X/gif-abstract0/img8.gif){kind=small} the corresponding Borel full groups. Modulo the obvious counterexamples, we show that ![$ [G] cong [H] Leftrightarrow E_G^X cong_B E_H^Y$](http://www.ams.org/proc/2007-135-02/S0002-9939-06-08542-X/gif-abstract0/img9.gif){kind=small} . |
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