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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the existence of minimal dynamical systems, their orbit and minimalorbit-breaking equivalence relations, and their applications to C*-algebras andK-theory. We show that given any finite CW-complex there exists a space withthe same K-theory and cohomology that admits a minimal homeomorphism. The proofrelies on the existence of homeomorphisms on point-like spaces constructed bythe authors in previous work, together with existence results for skew productsystems due to Glasner and Weiss. To any minimal dynamical system one canassociate minimal equivalence relations by breaking orbits at small subsets.Using Renault's groupoid C*-algebra construction we can associate K-theorygroups to minimal dynamical systems and orbit-breaking equivalence relations.We show that given arbitrary countable abelian groups $G_0$ and $G_1$ we canfind a minimal orbit-breaking relation such that the K-theory of the associatedC*-algebra is exactly this pair. These results have important applications tothe Elliott classification program for C*-algebras. In particular, we make astep towards determining the range of the Elliott invariant of the C*-algebrasassociated to minimal dynamical systems with mean dimension zero and theirminimal orbit-breaking relations

Constructions in minimal amenable dynamics and applications to the classification of $\mathrm{C}^*$-algebras