论文标题
第一个$ \ ell^2 $ -betti数字和正确的近端
First $\ell^2$-Betti numbers and proper proximality
论文作者
论文摘要
我们表明，对于一个可数的精确组，具有正面的$ \ ell^2 $ -betti编号意味着在这种意义上\ cite {boiope21}。这是通过显示出非侧面近端基团的伯努利偏移的共生超晶体结果来实现的。我们还获得了可数，不可义的，i.c.c.的伯努利偏移，精确的，非偏向的近端组是oe-superrigid。
We show that for a countable exact group, having positive first $\ell^2$-Betti number implies proper proximality in this sense of \cite{BoIoPe21}. This is achieved by showing a cocycle superrigidty result for Bernoulli shifts of non-properly proximal groups. We also obtain that Bernoulli shifts of countable, nonamenable, i.c.c., exact, non-properly proximal groups are OE-superrigid.
