Rokhlin dimension for flows

Abstract

We introduce a notion of Rokhlin dimension for one parameter automorphism groups of C*-algebras. This generalizes Kishimoto's Rokhlin property for flows, and is analogous to the notion of Rokhlin dimension for actions of the integers and other discrete groups introduced by the authors and Zacharias in previous papers. We show that finite nuclear dimension and absorption of a strongly self-absorbing C*-algebra are preserved under forming crossed products by flows with finite Rokhlin dimension, and that these crossed products are stable. Furthermore, we show that a flow on a commutative C*-algebra arising from a free topological flow has finite Rokhlin dimension, whenever the spectrum is a locally compact metrizable space with finite covering dimension. For flows that are both free and minimal, this has strong consequences for the associated crossed product C*-algebras: Those containing a non-zero projection are classified by the Elliott invariant (for compact manifolds this consists of topological K-theory together with the space of invariant probability measures and a natural pairing given by the Ruelle-Sullivan map).

arXiv comment67 pages. Minor changes from previous version. To appear, Comm. Math. Phys

References in corpus (7)

• Pure Point Dynamical and Diffraction Spectra
• Nuclear dimension and Z-stability
• Mean Dimension & Jaworski-type Theorems
• Nuclear dimension, Z-stability, and algebraic simplicity for stably projectionless C*-algebras
• The Rokhlin dimension of topological Z^m-actions
• The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras
• Topological Bragg Peaks And How They Characterise Point Sets

Cited by in corpus (5)

• Rokhlin dimension for actions of residually finite groups
• On a categorical framework for classifying C*-dynamics up to cocycle conjugacy
• The classification of Rokhlin flows on C*-algebras
• Rokhlin dimension: absorption of model actions
• Nuclear dimension of crossed products associated to partial dynamical systems