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AF-algebras and topology of mapping tori

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Abstract

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.

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Authors and Affiliations

  1. The Fields Institute for Research in Mathematical Sciences, University of Toronto, College Street 222, Toronto, Ontario, M5T 3J1, Canada

    Igor Nikolaev

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  1. Igor Nikolaev
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Correspondence to Igor Nikolaev.

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In memory of Dmitrii Viktorovich Anosov

Partially supported by NSERC.

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Nikolaev, I. AF-algebras and topology of mapping tori. Czech Math J 65, 1069–1083 (2015). https://doi.org/10.1007/s10587-015-0228-8

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  • DOI: https://doi.org/10.1007/s10587-015-0228-8

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