# $AF$-algebras and topology of mapping tori

Czechoslovak Mathematical Journal (2015)

- Volume: 65, Issue: 4, page 1069-1083
- ISSN: 0011-4642

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topNikolaev, Igor. "$AF$-algebras and topology of mapping tori." Czechoslovak Mathematical Journal 65.4 (2015): 1069-1083. <http://eudml.org/doc/276159>.

@article{Nikolaev2015,

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.},

author = {Nikolaev, Igor},

journal = {Czechoslovak Mathematical Journal},

keywords = {Anosov diffeomorphism; $AF$-algebra},

language = {eng},

number = {4},

pages = {1069-1083},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {$AF$-algebras and topology of mapping tori},

url = {http://eudml.org/doc/276159},

volume = {65},

year = {2015},

}

TY - JOUR

AU - Nikolaev, Igor

TI - $AF$-algebras and topology of mapping tori

JO - Czechoslovak Mathematical Journal

PY - 2015

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 65

IS - 4

SP - 1069

EP - 1083

AB - 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.

LA - eng

KW - Anosov diffeomorphism; $AF$-algebra

UR - http://eudml.org/doc/276159

ER -

## References

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