The C*-algebra of a vector bundle
Abstract
We prove that the Cuntz-Pimsner algebra O(E) of a vector bundle E over a compact metrizable space X is determined up to an isomorphism of C(X)-algebras by the ideal (1-[E])K(X) of the K-theory ring K(X). Moreover, if E and F are vector bundles of rank >1, then a unital embedding of C(X)-algebras of O(E) into O(F) exists if and only if 1-[E] is divisible by 1-[F] in the ring K(X). We introduce related, but more computable K-theory and cohomology invariants for O(E) and study their completeness. As an application we classify the unital separable continuous fields with fibers isomorphic to the Cuntz algebra O(m+1) over a finite connected CW complex X of dimension d< 2m+4 provided that the cohomology of X has no m-torsion.
Keywords
Cite
@article{arxiv.1004.1722,
title = {The C*-algebra of a vector bundle},
author = {Marius Dadarlat},
journal= {arXiv preprint arXiv:1004.1722},
year = {2010}
}
Comments
22 pages, the case of line bundles was added to the paper