The C*-algebra of a Vector Bundle
نویسنده
چکیده
We prove that the Cuntz-Pimsner algebra OE of a vector bundle E of rank ≥ 2 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 ≥ 2, then a unital embedding of C(X)-algebras OE ⊂ OF 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 OE and study their completeness. As an application we classify the unital separable continuous fields with fibers isomorphic to the Cuntz algebra Om+1 over a finite connected CW complex X of dimension d ≤ 2m + 3 provided that the cohomology of X has no m-torsion.
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