turkmath.org

Topological K-theory is perhaps the most prominent example of a generalized cohomology theory, i.e it satisfies all the axioms in the axiomatic definition given by Eilenberg and Steenrod for a cohomology theory except for the dimension axiom. Among its impressive achievements in the past one can name some important and deep theorems of mathematics like Atiyah-Singer index theorem, Adams' solution of the vector field problem on spheres, solution of Hopf invariant one problem, etc. In this talk for a general audience, we will give a brief overview of the basic notions of this theory and mention some of the important applications in the past. We will also present more recent applications in geometry and topology.