Isomorphism of Borel full groups
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- by Benjamin D. Miller and Christian Rosendal PDF
- Proc. Amer. Math. Soc. 135 (2007), 517-522 Request permission
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
- 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, DOI 10.1017/CBO9780511735264
- Alexander S. Kechris and Benjamin D. Miller, Topics in orbit equivalence, Lecture Notes in Mathematics, vol. 1852, Springer-Verlag, Berlin, 2004. MR 2095154, DOI 10.1007/b99421
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
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 517-522
- MSC (2000): Primary 03E15
- DOI: https://doi.org/10.1090/S0002-9939-06-08542-X
- MathSciNet review: 2255298