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Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Isomorphism of Borel full groups

Author(s): Benjamin D. Miller; Christian Rosendal
Journal: Proc. Amer. Math. Soc. 135 (2007), 517-522.
MSC (2000): Primary 03E15
Posted: 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:

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
Email: bdm@math.ucla.edu

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
Email: rosendal@math.uiuc.edu

DOI: 10.1090/S0002-9939-06-08542-X
PII: S 0002-9939(06)08542-X
Received by editor(s): June 20, 2005
Received by editor(s) in revised form: September 6, 2005.
Posted: August 8, 2006
Additional Notes: The first author was supported in part by NSF VIGRE Grant DMS-0502315.
Communicated by: Julia Knight
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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