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Let $\mathcal{G}$ be a strict topological $2$-group, i.e. a strict $2$-category with a single object, a space of invertible $1$-morphisms, a space of invertible $2$-morphisms and continuous structure …

What is the standard reference for the fact that the classifying space of a strict monoidal category is a topological monoid with respect to the operation induced by the tensor product? EDIT: The fir …

Let $G= SU(n)$ and let $\mathbb{T}$ be the maximal torus in $G$ given by diagonal matrices. We have $$ H^*(G,\mathbb{Q}) \cong \Lambda_{\mathbb{Q}}[x_3, x_5, \dots, x_{2n-1}] \ . $$ Now consider the …

This is not necessarily an answer, but it was too long for a comment: Note that for any separable unital $C^*$-algebra $A$ its suspension $SA := C_0(\mathbb{R}) \otimes A$ is quasidiagonal. This can …

Let me add some new-ish books to the mix that I liked and deal with some topics in $C^*$-algebras that have picked up some steam in recent years: If you want an introduction to the state of the art …

There is a book by Herbert Schröder called "K-Theory for Real C*-algebras and Applications", which can be found on mathscinet and has a Google Books entry (sadly without preview).

In the world of $C^*$-algebras, there are cases, where a homomorphism $f \colon K_0(A) \to K_0(B)$ is induced not only by a bimodule, but by an honest $*$-homomorphism. For example, if $A$ is a separa …

My reference for this is now Corollary 11.7 in J. P. May. The geometry of iterated loop spaces. Springer-Verlag, Berlin, 1972. Lectures Notes in Mathematics, Vol. 271.

Let $G$ and $H$ be two topological groupoids. Recall that a morphism $F \colon H \to G$ is called an essential equivalence, if the map $t \circ \pi_1 \colon G_1 \times_{G_0} H_0 \to G_0$ is an open …