Skip to main content
Log in

Topological complexity of certain classes of C*-algebras

  • Published:
Russian Journal of Mathematical Physics Aims and scope Submit manuscript

Abstract

We compute the topological complexity for some important classes of noncommutative C*-algebras: AF algebras, AI algebras, and even Cuntz algebras.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. O. Yu. Aristov, “On the Homotopy Equivalence of Simple AI-Algebras,” Mat. Sb. 190 (2), 3–30 (1999) [Sb. Math. 190 (2), 165–191 (1999)].

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Dadarlat, “The Homotopy Groups of the Automorphism Group of Kirchberg Algebras,” J. Noncommut. Geom. 1, 113–139 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Dadarlat and T. A. Loring, “A Universal Multicoefficient Theorem for the Kasparov Groups,” Duke Math. J. 84, 355–377 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Dadarlat and A. Nemethi, “Shape Theory and Connective K-Theory,” J. Operator Theory 23, 207–291 (1990).

    MathSciNet  MATH  Google Scholar 

  5. M. Dadarlat and W. Winter, “On the KK-Theory of Strongly Self-Absorbing C*-Algebras,” Mathematica Scandinavica, 95–107 (2009).

    Google Scholar 

  6. K. R. Davidson, C*-Algebras by Examples (Fields Institute Monographs, Vol. 6., AMS, 1996).

    Book  MATH  Google Scholar 

  7. E. Dyer and A. T. Vasquez, “Some Small Aspherical Spaces,” J. Austral. Math. Soc. 16, 332–352 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  8. G. A. Elliott and G. Gong, “On the Classification of C*-Algebras of Real Rank Zero II,” Ann. Math. 144 (3), 497–610 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Farber, “Topological Complexity of Motion Planning,” Discrete Comput. Geom. 29, 211–221 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  10. L. Fuchs, Infinite Abelian Groups, Vol. I (Academic Press, Academic Press, New York–London, 1970).

    MATH  Google Scholar 

  11. V. Manuilov, “A Noncommutative Version of Farber‘s Topological Complexity,” Topol. Methods Nonlinear Anal. 49 (4), to appear (2017).

    Google Scholar 

  12. I. F. Putnam, “An Extension Theorem for the K-Theory of C*-Algebras,” J. Oper. Theory 38, 151–171 (1997).

    MATH  Google Scholar 

  13. M. Rørdam and E. Størmer, Classification of Nuclear C*-Algebras. Entropy in Operator Algebras (Springer, Encycl. Math. Sci. 126 (VII), 2002).

    Book  MATH  Google Scholar 

  14. J. Rosenberg and C. Schochet, “The Künneth Theorem and the Universal Coefficient Theorem for Kasparov’s Generalized K-Functor,” Duke Math. J. 55, 431–474 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  15. C. Schochet, “Topological Methods for C*-Algebras II,” Pasific Journal of Mathematics 98 (2), 443–458 (1982).

    Article  MATH  Google Scholar 

  16. K. Thomsen, Classifying C*-Algebras (preprint, 2005).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. I. Korchagin.

Additional information

The author acknowledges the partial support by the RFBR grant no. 16-01-00357.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Korchagin, A.I. Topological complexity of certain classes of C*-algebras. Russ. J. Math. Phys. 24, 347–353 (2017). https://doi.org/10.1134/S1061920817030086

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1061920817030086

Navigation