Connes' Rigidity Conjecture for ICC Property (T) Groups
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Statement
Connes' rigidity conjecture asks whether an ICC group with Kazhdan's property (T) is determined by its group von Neumann algebra. Disproved for this class: two explicit countable discrete groups and , both ICC and property (T), are non-isomorphic as groups while .
Context
Settles the ICC property (T) case. The paper records that the result was obtained independently of and concurrently with work by OpenAI.
Connes' rigidity conjecture is among the best-known open problems in von Neumann algebras, and W*-superrigidity for property (T) groups has organised a substantial part of that literature since the 1980s.
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The AI use statement says the construction underlying the main result was found mainly by GPT-5.6 Sol, Codex and the Danus multi-agent research system, under the author's mathematical guidance, with Lean 4.32.1 used alongside.
Settles the ICC property (T) case. The paper records that the result was obtained independently of and concurrently with work by OpenAI.
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