Geodesic
The structure of cocycles of pseudo-homeomorphism groups
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2000) no. 2, pp. 209-218 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\Gamma$ be a countable group acting ergodically as pseudo-homeomorphisms on a perfect Polish space $X$. It is proved that, modulo a meagre subset of $X$, any two ergodic cocycles $\alpha$ and $\beta$ of this action with values in a countable group $G$ are weakly equivalent. This result further applied to prove the outer conjugacy of a countable groups of pseudo-homeomorphisms from the normalizer $N[\Gamma]$ of a full group $[\Gamma]$. 
@article{JMAG_2000_7_2_a5,
     author = {V. Kulagin},
     title = {The structure of cocycles of pseudo-homeomorphism groups},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {209--218},
     year = {2000},
     volume = {7},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2000_7_2_a5/}
}
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V. Kulagin. The structure of cocycles of pseudo-homeomorphism groups. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2000) no. 2, pp. 209-218. http://geodesic.mathdoc.fr/item/JMAG_2000_7_2_a5/