| Title:
|
$AF$-algebras and topology of mapping tori (English) |
| Author:
|
Nikolaev, Igor |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
1069-1083 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Anosov diffeomorphism |
| Keyword:
|
$AF$-algebra |
| MSC:
|
46L85 |
| MSC:
|
55S35 |
| idZBL:
|
Zbl 06537711 |
| idMR:
|
MR3441336 |
| DOI:
|
10.1007/s10587-015-0228-8 |
| . |
| Date available:
|
2016-01-13T09:24:14Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144793 |
| . |
| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
[7] Morandi, P.: Field and Galois Theory.Graduate Texts in Mathematics 167 Springer, New York (1996). Zbl 0865.12001, MR 1410264, 10.1007/978-1-4612-4040-2 |
| Reference:
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| Reference:
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| Reference:
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| . |
