W$^*$-superrigidity for wreath products with groups having positive first $\ell^2$-Betti number

Mihaita Berbec

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arXiv · 1403.7110

W$^*$-superrigidity for wreath products with groups having positive first $\ell^2$-Betti number

Mihaita Berbec

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Abstract

In [BV12] we have proven that, for all hyperbolic groups and for all non-trivial free products $\Gamma$, the left-right wreath product group $G:=(Z/2Z)^{(\Gamma)} \rtimes (\Gamma \times \Gamma)$ is W$^*$-superrigid. In this paper, we extend this result to other classes of countable groups. More precisely, we prove that for weakly amenable groups $\Gamma$ having positive first $\ell^2$-Betti number, the same wreath product $G$ is W$^*$-superrigid.

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BibTeX RIS

Mihaita Berbec. 2014-03-27. W$^*$-superrigidity for wreath products with groups having positive first $\ell^2$-Betti number. https://arxiv.org/abs/1403.7110

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