Sorin Popa - Academia.edu (original) (raw)

Papers by Sorin Popa

Journal of Functional Analysis, 2006

We introduce the outer conjugacy invariants S(), S s () for cocycle actions of discrete groups G ... more We introduce the outer conjugacy invariants S(), S s () for cocycle actions of discrete groups G on type II 1 factors N, as the set of real numbers t > 0 for which the amplification t of can be perturbed to an action, respectively, to a weakly mixing action. We calculate explicitly S(), S s () and the fundamental group of , F(), in the case G has infinite normal subgroups with the relative property (T) (e.g., when G itself has the property (T) of Kazhdan) and is an action of G on the hyperfinite II 1 factor by Connes-StZrmer Bernoulli shifts of weights {t i } i. Thus, S s () and F() coincide with the multiplicative subgroup S of R * + generated by the ratios {t i /t j } i,j , while S() = Z * + if S = {1} (i.e. when all weights are equal), and S() = R * + otherwise. In fact, we calculate all the "1-cohomology picture" of t , t > 0, and classify the actions (, G) in terms of their weights {t i } i. In particular, we show that any 1-cocycle for (, G) vanishes, modulo scalars, and that two such actions are cocycle conjugate iff they are conjugate. Also, any cocycle action obtained by reducing a Bernoulli ଁ A preliminary version of this paper was circulated as MSRI preprint No. 2001-2005 under the title "A rigidity result for actions of property (T) groups by Bernoulli shifts". The present version of the paper was circulated as a UCLA preprint since November 2001.

Journal of Functional Analysis, 2006

We introduce the outer conjugacy invariants S(), S s () for cocycle actions of discrete groups G ... more We introduce the outer conjugacy invariants S(), S s () for cocycle actions of discrete groups G on type II 1 factors N, as the set of real numbers t > 0 for which the amplification t of can be perturbed to an action, respectively, to a weakly mixing action. We calculate explicitly S(), S s () and the fundamental group of , F(), in the case G has infinite normal subgroups with the relative property (T) (e.g., when G itself has the property (T) of Kazhdan) and is an action of G on the hyperfinite II 1 factor by Connes-StZrmer Bernoulli shifts of weights {t i } i. Thus, S s () and F() coincide with the multiplicative subgroup S of R * + generated by the ratios {t i /t j } i,j , while S() = Z * + if S = {1} (i.e. when all weights are equal), and S() = R * + otherwise. In fact, we calculate all the "1-cohomology picture" of t , t > 0, and classify the actions (, G) in terms of their weights {t i } i. In particular, we show that any 1-cocycle for (, G) vanishes, modulo scalars, and that two such actions are cocycle conjugate iff they are conjugate. Also, any cocycle action obtained by reducing a Bernoulli ଁ A preliminary version of this paper was circulated as MSRI preprint No. 2001-2005 under the title "A rigidity result for actions of property (T) groups by Bernoulli shifts". The present version of the paper was circulated as a UCLA preprint since November 2001.