An isomorphism of the free group factors
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 \(\mathbb R_{\gt 0}\).
Cite
@misc{OAI:An-isomorphism-of-the-free-group-factors-September-23-2026,
author = {{OpenAI}},
title = {{An isomorphism of the free group factors}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/An-isomorphism-of-the-free-group-factors-September-23-2026/An-isomorphism-of-the-free-group-factors-September-23-2026.pdf}{OAI:An-isomorphism-of-the-free-group-factors-September-23-2026}},
year = {2026}
}