English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Under suitable conditions, a substitution tiling gives rise to a Smale space,from which three equivalence relations can be constructed, namely the stable,unstable, and asymptotic equivalence relations. We denote with $S$, $U$, and$A$ their corresponding $C^*$-algebras in the sense of Renault. In this articlewe show that the $K$-theories of $S$ and $U$ can be computed from thecohomology and homology of a single cochain complex with connecting maps fortilings of the line and of the plane. Moreover, we provide formulas to computethe $K$-theory for these three $C^*$-algebras. Furthermore, we show that the$K$-theory groups for tilings of dimension 1 are always torsion free. Fortilings of dimension 2, only $K_0(U)$ and $K_1(S)$ can contain torsion.

On the K-theory of C*-algebras for substitution tilings (a pedestrian version)