Ulrich Pennig: Locally trivial W*-bundles

Tracially continuous W*-bundles were introduced by Ozawa. Their study was motivated by work on the structure and classification of simple, nuclear C*-algebras. They are similar in spirit to C(X)-algebras. Their fibres, however, are tracial von Neumann algebras. In joint work with Sam Evington, we prove that a tracially continuous W*-bundle over a compact Hausdorff space with all fibres isomorphic to the hyperfinite type II₁-factor R that is locally trivial already has to be globally trivial. The proof uses the contractibility of the automorphism group Aut(R) shown by Popa and Takesaki. There is no restriction on the covering dimension of the underlying space.