URegina Topology and Geometry Seminar: Martin Frankland

Topological K-theory is an invariant of spaces based on vector bundles. We will review vector bundles and their representability by Grassmannians. We will then introduce the group K^0(X), which measures to what extent vector bundles on X can be non-trivial. Finally, Bott periodicity will allow us to extend the group K^0(X) to a cohomology theory.