Minimal Dynamics and K-theoretic Rigidity: Elliott's Conjecture
Operator Algebras
2009-03-25 v1 Dynamical Systems
Abstract
Let X be an infinite, compact, metrizable space of finite covering dimension and h a minimal homeomorphism of X. We prove that the crossed product of C(X) by h absorbs the Jiang-Su algebra tensorially and has finite nuclear dimension. As a consequence, these algebras are determined up to isomorphism by their graded ordered K-theory under the necessary condition that their projections separate traces. This result applies, in particular, to those crossed products arising from uniquely ergodic homeomorphisms.
Cite
@article{arxiv.0903.4133,
title = {Minimal Dynamics and K-theoretic Rigidity: Elliott's Conjecture},
author = {Andrew S. Toms and Wilhelm Winter},
journal= {arXiv preprint arXiv:0903.4133},
year = {2009}
}
Comments
19 pages