$K$-theory over $C^{*}$-algebras

Volume 76 / 2007

Alexandr S. Mishchenko Banach Center Publications 76 (2007), 245-266 MSC: Primary 57Rxx, 55Rxx, 19Lxx; Secondary 19Kxx, 46L80, 46M20. DOI: 10.4064/bc76-0-13


The contents of the article represents the minicourse which was delivered at the 7th conference “Geometry and Topology of Manifolds. The Mathematical Legacy of Charles Ehresmann”, B/edlewo (Poland), 8.05.2005 – 15.05.2005. The article includes the description of the so called Hirzebruch formula in different aspects which lead to a basic list of problems related to noncommutative geometry and topology. In conclusion, two new problems are presented: about almost flat bundles and about the Noether decomposition of the Fredholm operators which may not admit the adjoint operator.


  • Alexandr S. MishchenkoDepartment of Mechanics and Mathematics
    Moscow State University
    119992 Moscow, Russia

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