Take the 2-minute tour ×  If we consider algebra bundles over X
where the fiber is an algebra of bounded operators in a
separable Hilbert space H over the complex numbers. I learn from
"Isomorphism Classification of Operator Algebra Bundles" (D.
Husemoller) that we can use $H^{3}(X, Z)$ to classify these
bundles if the fiber is $M_n(C)$, $B(H)$ or $K$(the algebra of
compact operators). Now I want to know is there any result on
how to classify the operator algebra bundles if the fiber is
II$_1$ factor?  share|improve this question In the examples you
cite, we know what the groups of automorphisms of the algebras
are: some sort of projective unitary group, and the classifying
spaces of these are well understood. I don't know what $Aut(A)$
is for a general vN algebra $A$ (or even just a $II_1$ factor),
but calculating $BAut(A)$ is the way to go. –  David Roberts Feb
28 '13 at 5:53  1 Answer 1  The answer to your question depends
of course heavily on the topology that you use for the
automorphism group of the $II