Michael Atiyah’s work in algebraic topology

Abstract

In 1960 algebraic topology was at the centre of the mathematical stage, but Michael Atiyah burst into the field and changed its focus and its language. I describe his work of the following decade and its influence, keeping to the themes of K K -theory and generalized cohomology to minimise the overlap with Dan Freed’s account of Atiyah’s work on index theory, which also appears in this issue.