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

### Volume 76 / 2007

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

#### Abstract

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.