Groups and Operator Algebras Seminar

Speaker:  David Jekel (U of Copenhagen)

Title:  The unitary group of a II₁-factor is SOT-contractible

Abstract:  I 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 I_n direct summands (n < infinity). 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.  With enough time, I will present some of the older results as well.