arXiv subjects

Sihan Wei

Publications and source records attributed to Sihan Wei.

4 recordsLinked to original sources

arXiv2023

A generalization of topological Rokhlin dimension and an embedding result

We generalize Gabor's notion of topological Rokhlin dimension of $\mathbb{Z}^k$-actions on compact metric space to a class of general discrete countable amenable group actions which involves the approximate subgroup structure. Then with this generalization, we conclude the finiteness of topological Rokhlin dimension, amenability dimension, dynamic asymptotic dimension and also of the nuclear dimension of the crossed product. An embedding result is also obtained, regarding those systems with mean dimension less that $m/2$ and with a finite-dimensional free factor.

math.OA↗

arXiv2023

Dimensions associated with surjective local homeomorphisms and subshifts with low complexity

We prove that the Cuntz-Pimsner algebra associated to any surjective aperiodic one-sided subshift with finitely many left special elements has finite nuclear dimension, which is especially the case for every surjective aperiodic subshift with nonsuperlinear-growth complexity. As a generalization, we define the notions of left speical set, the topological Rokhlin dimension, the tower dimension and the amenability dimension for every local homeomorphism. Then we turn to prove that, for every surjective local homeomorphism with a finite left special set consisting of isolated points, these dimensions along with the dynamic asymptotic dimension are all finite.

math.OA↗

arXiv2023

A note on the nuclear dimension of Cuntz-Pimsner $C^*$-algebras associated with minimal shift spaces

For every one-sided shift space $X$ over a finite alphabet, left special elements are those points in $X$ having at least two preimages under the shift operation. In this paper, we show that the Cuntz-Pimsner $C^*$-algebra $\mathcal{O}_X$ has nuclear dimension 1 when $X$ is minimal and the number of left special elements in $X$ is finite. This is done by describing thoroughly the cover of $X$ which also recovers an exact sequence, discovered before by T. Carlsen and S. Eilers.

math.OA↗

arXiv2021

Approximate $K$-conjugacies and $C^*$-approximate conjugacies of minimal dynamical systems

In this article, we extend H. Matui and H. Lin's notions of approximate $K$-conjugacies and $C^*$-strongly approximate conjugacies to general minimal dynamical systems. In particular, upon modifying a result of the existence of minimal skew products, we answer a question of H. Lin and show that, associated with any Cantor minimal system $(K,\tildeα)$, there is a class $R_0(\tildeα)$ of minimal skew products on $K\timesΩ$, such that for any two rigid homeomorphisms $α\in R_0(\tildeα)$ and $β\in R_0(\tildeβ)$, the notions of approximate $K$-conjugacy and $C^*$-strongly approximate conjugacy coincide, which are also equivalent to a $K$-version of Tomiyama's commutative diagram, where $Ω$ is an (infinite) connected finite CW-complex with torsion free $K$-groups and the so-called Lipschitz-minimal-property (LMP).

math.DS↗