On a Cuntz-Krieger functor

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New Zealand Journal of Mathematics

Vol. 39, (2009), Pages 165-169


Igor V. Nikolaev

The Fields Institute for Mathematical Sciences

Toronto, ON

Canada

mailto:igor.v.nikolaev@gmail.com






Abstract We construct a covariant functor from the topological torus bundles to the so-called Cuntz-Krieger algebras; the functor maps homeomorphic bundles into the stably isomorphic Cuntz-Krieger algebras. It is shown, that the K-theory of the Cuntz-Krieger algebra encodes torsion of the first homology group of the bundle. We illustrate the result by examples.

Keywords torus bundle, Cuntz-Krieger algebra.

Classification (MSC2000) Primary: 46L; 57M.

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