This was a byproduct of my Master’s thesis.
Abstract
Atiyah’s -theory from his “-Theory and Reality” paper (1966) establishes a unified view of complex and real -theory and in particular gives a quite elegant proof of the periodicity theorem for . In this expository talk I will try to give a quick overview of the basic properties of this theory and afterwards focus on the proof of Bott periodicity in the real case via -theory. Contrary to the approach of the original paper we will also encounter a proof that the Atiyah–Bott–Shapiro homomorphism is an isomorphism during this discussion.
The slides are available here