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Isomorphism of Borel full groups

Authors: Benjamin D. Miller and Christian Rosendal
Journal: Proc. Amer. Math. Soc. 135 (2007), 517-522
MSC (2000): Primary 03E15
Published electronically: August 8, 2006
MathSciNet review: 2255298
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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that $ G$ and $ H$ are Polish groups which act in a Borel fashion on Polish spaces $ X$ and $ Y$. Let $ E_G^X$ and $ E_H^Y$ denote the corresponding orbit equivalence relations, and $ [G]$ and $ [H]$ the corresponding Borel full groups. Modulo the obvious counterexamples, we show that $ [G] \cong [H] \Leftrightarrow E_G^X \cong_B E_H^Y$.

References [Enhancements On Off] (What's this?)

  • 1. Howard Becker and Alexander S. Kechris, The descriptive set theory of Polish group actions, London Mathematical Society Lecture Note Series, vol. 232, Cambridge University Press, Cambridge, 1996. MR 1425877 (98d:54068)
  • 2. A.S. Kechris and B.D. Miller, Topics in orbit equivalence, Lecture Notes in Mathematics, vol. 1852, Springer-Verlag, Berlin, 2004. MR 2095154 (2005f:37010)

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Additional Information

Benjamin D. Miller
Affiliation: Department of Mathematics, University of California Los Angeles, Box 951555, Los Angeles, California 90095-1555

Christian Rosendal
Affiliation: Department of Mathematics 253-37, California Institute of Technology, Pasadena, California 91125
Address at time of publication: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street (MC-382), Urbana, Illinois 61801-2975

Received by editor(s): June 20, 2005
Received by editor(s) in revised form: September 6, 2005
Published electronically: August 8, 2006
Additional Notes: The first author was supported in part by NSF VIGRE Grant DMS-0502315.
Communicated by: Julia Knight
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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