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This paper demonstrates the SOT-contractibility of any SOT-separable II1 factor's unitary group, implying similar results for von Neumann algebras.
We show that the unitary group of any SOT-separable II₁ factor M, with the strong operator topology, is contractible. Combined with several old results, this implies that the same is true for any SOT-separable von Neumann algebra with no type Iₙ direct summands (n < ∞). The proof for the II₁-factor case uses regularization via free convolution and Popa's theorem on the existence of approximately free Haar unitaries in II₁ factors.
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David Jekel (2025) studied this question.
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