Geodesic
$AF$-algebras and topology of mapping tori
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 1069-1083

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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.
DOI : 10.1007/s10587-015-0228-8
Classification : 46L85, 55S35
Keywords: Anosov diffeomorphism; $AF$-algebra 
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Nikolaev, Igor. $AF$-algebras and topology of mapping tori. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 1069-1083. doi: 10.1007/s10587-015-0228-8

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