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3 votes
0 answers
84 views

Cohomological counterpart of the K-theory of the Roe C*-algebra in non-periodic systems

In crystalline insulating quantum systems the dynamics of electrons is governed by a Schrödinger operator which is periodic with respect to a Bravais lattice $\Gamma\cong \mathbb{Z}^d$ and whose ...
3 votes
1 answer
159 views

K-group properties of quasi-diagonal $C^*$-algebras

Let $A$ be a separable unital quasidiagonal $C^*$-algebra. What can be said about the $K$-theory of $A$, for example some properties? Especially, are there some criterions to decide whether or not $K_*...
1 vote
0 answers
133 views

K-Exactness for groups and C*-algebras

We say that a C*-algebra $A$ is K-exact, if for any exact sequence of C*-algebras $0\rightarrow I\rightarrow B\rightarrow B/I\rightarrow0$, the sequences $K_i(I\otimes_{min}A)\rightarrow K_i(B\...
8 votes
2 answers
437 views

Injectivity of the Baum-Connes assembly map for locally compact groups

Skandalis, Tu and Yu in "The coarse Baum-Connes conjecture and groupoids" proved that: Let $\Gamma$ be a countable group with a proper left-invariant metric $d$. If $\Gamma$ admits a uniform ...
0 votes
1 answer
287 views

The stabilized homotopy category of graded C* algebra

Hi everyone On page 147 of the note "Group C*-Algebras and K-theory" by N.Higson and E.Guentner there are something about the stabilized homotopy category of graded C* algebra, which is a category ...