Contractibility of unitary groups of II-1 factors
Question: Let be a -factor. Is the unitary group contractible when equipped with the strong operator topology? Background/Motivation: By Kuiper’s theorem, if is an infinite-dimensional Hilbert space, then the unitary group of the -factor is contractible in the norm topology. This was generalized by Breuer [1] to (certain) and von Neumann algebras, and eventually Brüning-Willgerodt… Weiterlesen »