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Outer automorphism groups of some equivalence relations
Commentarii Mathematici Helvetici
Let R a be countable ergodic equivalence relation of type II 1 on a standard probability space (X, µ). The group Out R of outer automorphisms of R consists of all invertible Borel measure preserving maps of the space which map R-classes to R-classes modulo those which preserve almost every R-class. We analyze the group Out R for relations R generated by actions of higher rank lattices, providing general conditions on finiteness and triviality of Out R and explicitly computing Out R for thedoi:10.4171/cmh/10 fatcat:smep346cefe4neoumpbymzf5xa