On a Cuntz-Krieger functor

TL;DR

This paper introduces a functor linking topological torus bundles to Cuntz-Krieger algebras, revealing how algebraic invariants encode topological torsion, with illustrative examples.

Contribution

It constructs a covariant functor from topological torus bundles to Cuntz-Krieger algebras, connecting topological and algebraic invariants.

Findings

K-theory of Cuntz-Krieger algebra encodes torsion in the first homology group

Homeomorphic bundles map to stably isomorphic Cuntz-Krieger algebras

Examples demonstrate the correspondence between topology and algebra

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.