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Approximate equivalence of group actions

Published online by Cambridge University Press:  24 January 2017

ANDREAS NÆS AASERUD  and
SORIN POPA
ANDREAS NÆS AASERUD
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA email andreas.naes.aaserud@gmail.com, popa@math.ucla.edu
SORIN POPA
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA email andreas.naes.aaserud@gmail.com, popa@math.ucla.edu
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Abstract

We consider several weaker versions of the notion of conjugacy and orbit equivalence of measure preserving actions of countable groups on probability spaces, involving equivalence of the ultrapower actions and asymptotic intertwining conditions. We compare them with the other existing equivalence relations between group actions, and study the usual type of rigidity questions around these new concepts (superrigidity, calculation of invariants, etc).

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 4 , June 2018 , pp. 1201 - 1237
Copyright
© Cambridge University Press, 2017 

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