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.Comment: to appear Czechoslovak Math. 

D. V. Anosov

E. G. Effros

H. B. Lawson Jr.

Igor Nikolaev

J. F. Plante

L. Bernstein

M. Bauer

O. Bratteli

P. Morandi

S. Smale

W. P. Thurston

English

arXiv

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Czechoslovak Mathematical Journal

AF-algebras and topology of mapping tori

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

Nikolaev, Igor

Czech digital mathematics library

$AF$-algebras and topology of mapping tori

Institute of Mathematics AS CR, v. v. i.

AF-algebras and topology of mapping tori

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Crossref

Czech digital mathematics library

Institute of Mathematics AS CR, v. v. i.