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arXiv · 2608.02327

ICC property (T) groups without W$^*$-superrigidity

Shuoxing Zhou
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Abstract

We construct two explicit countable discrete groups $\Gamma_1$ and $\Gamma_2$ that are both ICC and have Kazhdan's property (T). Although $\Gamma_1$ and $\Gamma_2$ are not isomorphic as groups, their group von Neumann algebras are isomorphic: $L(\Gamma_1)\cong L(\Gamma_2)$. This provides a counterexample to Connes' rigidity conjecture for ICC property (T) groups. This result was obtained with assistance from GPT-5.6 Sol, independently of and concurrently with work by OpenAI.

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Shuoxing Zhou. 2026-08-03. ICC property (T) groups without W$^*$-superrigidity. https://arxiv.org/abs/2608.02327

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