Homotopy theory for C*-algebras
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Thu, 14/10/2010 12:00 |
Michael Groechenig (Oxford University Mathematical Institute) |
Junior Geometry and Topology Seminar  |
SR1 |
| The theory of C*-algebras provides a good realisation of noncommutative topology. There is a dictionary relating commutative C*-algebras with locally compact spaces, which can be used to import topological concepts into the C*-world. This philosophy fails in the case of homotopy, where a more sophisticated definition has to be given, leading to the notion of asymptotic morphisms. As a by-product one obtains a generalisation of Borsuk's shape theory and a universal boundary map for cohomology theories of C*-algebras. | |||