• Corpus ID: 253499187

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

  title={First \$\ell^2\$-Betti numbers and proper proximality},
  author={Changying Ding},
. 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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