\(AF\)-algebras and topology of mapping tori. (English) Zbl 1374.46054

Summary: The paper studies applications of \(C^*\)-algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of \(AF\)-algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding \(AF\)-algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension 2, 3 and 4. In conclusion, we consider two numerical examples illustrating our main results.


46L85 Noncommutative topology
55S35 Obstruction theory in algebraic topology
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