Principal Groupoid Models for Cuntz Algebras and their Dynamic Asymptotic Dimension

Abstract

We compute the dynamic asymptotic dimension of the principal groupoid models for the Cuntz algebras ${\mathcal{O}}_k$ for $2\le k<\infty$ that have arisen from work of Winter and the authors. Our method generalises to a wide class of Deaconu-Renault groupoids. As an application of our results, we prove that ${\mathcal{O}}_2$ has infinitely many non-conjugate C${}^{\ast }$-diagonals with Cantor spectrum, and we generalise this result to other Cuntz algebras by combining the main result with work of Kopsacheilis-Winter and Brown-Clark-Sierakowski-Sims.

16 pages