A F -algebras and topology of mapping tori

Igor Nikolaev

Czechoslovak Mathematical Journal (2015)

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

Abstract

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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 A F -algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding A F -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.

How to cite

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Nikolaev, 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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  7. Morandi, P., 10.1007/978-1-4612-4040-2, Graduate Texts in Mathematics 167 Springer, New York (1996). (1996) Zbl0865.12001MR1410264DOI10.1007/978-1-4612-4040-2
  8. Plante, J. F., Foliations with measure preserving holonomy, Ann. Math. (2) 102 (1975), 327-361. (1975) Zbl0314.57018MR0391125
  9. Smale, S., 10.1090/S0002-9904-1967-11798-1, Bull. Am. Math. Soc. 73 (1967), 747-817. (1967) Zbl0202.55202MR0228014DOI10.1090/S0002-9904-1967-11798-1
  10. Thurston, W. P., 10.1090/S0273-0979-1988-15685-6, Bull. Am. Math. Soc., New Ser. 19 (1988), 417-431. (1988) Zbl0674.57008MR0956596DOI10.1090/S0273-0979-1988-15685-6

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