Geodesic
On cocycles with values in group extensions. Generic results
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2000) no. 2, pp. 153-171 
Alexandre I. Danilenko. On cocycles with values in group extensions. Generic results. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2000) no. 2, pp. 153-171. http://geodesic.mathdoc.fr/item/JMAG_2000_7_2_a1/
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     author = {Alexandre I. Danilenko},
     title = {On cocycles with values in group extensions. {Generic} results},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {153--171},
     year = {2000},
     volume = {7},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2000_7_2_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $1\to A\to E\to G\to 1$ be a short exact sequence of locally compact groups, $A$ amenable. Given a recurrent $G$-valued cocycle $\omega$ of an ergodic nonsingular transformation, we consider the subset of those $E$-valued cocycles whose $G$-projection is $\omega$. It is proved that for a generic cocycle from this subset the restriction of the associated (Mackey) $E$-action to $A$ is trivial. This improves some results of K. Dajani (1991, 1993) and answers a question from her paper in Trans. Amer. Math. Soc. (1991).