# First $\ell^2$-Betti numbers and proper proximality

@inproceedings{Ding2022FirstN, title={First \$\ell^2\$-Betti numbers and proper proximality}, author={Changying Ding}, year={2022} }

. We show that for a countable exact group, having positive ﬁrst ℓ 2 -Betti number implies proper proximality in this sense of [BIP21]. This is achieved by showing a cocycle super-rigidty 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.

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