## When can’t spaces of correspondences distinguish type $II_{1}$ factors?

If $M$ is a type $II_{1}$ factor with trace $\tau$, let $Corr(M)$ denote the space of unitary equivalence classes of $M-M$ correspondences (binormal $M-M$ bimodules) equipped with Popa's analogue of Fell's topology. All details of the above can be found in here.

What are some examples of pairs of nonisomorphic type $II_{1}$ factors $M,N$ such that their associated spaces of correspondences $Corr(M), Corr(N)$ are homeomorphic?

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