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Isomorphism of the free group factors

Resolves the free group factor isomorphism problem:

L(\mathbb F_2)\cong L(\mathbb F_3)

, and hence all interpolated free group factors, including

L(\mathbb F_\infty)

, are isomorphic. Their common factor has fundamental group

\mathbb R_{\gt 0}

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An isomorphism of the free group factors

Sep 23, 2026·An-isomorphism-of-the-free-group-factors-September-23-2026.pdf

We solve the free group factor isomorphism problem affirmatively by proving that

L(\mathbb F_2)

and

L(\mathbb F_3)

are isomorphic as tracial von Neumann algebras. The classical free group factor alternative then implies that all interpolated free group factors, including

L(\mathbb F_\infty)

, are isomorphic and have fundamental group

\mathbb R_{\gt 0}

Full abstract

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OpenAI also released the model's reasoning trace for this result: reasoning trace (PDF).