A rigid hyperfinite type $\mathrm{II}_1$ factor

preprint2020arXivOpen access

We show that it is relatively consistent with ZFC that there exists a hyperfinite type $\mathrm{II}_1$ -factor of density character $\aleph_1$ which is not isomorphic to its opposite, does not have any outer automorphisms, and has trivial fundamental group.

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A rigid hyperfinite type $\mathrm{II}_1$ factor

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A rigid hyperfinite type II1\mathrm{II}_1II1​ factor

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A rigid hyperfinite type $\mathrm{II}_1$ factor