Bott Periodicity in Topological, Algebraic and Hermitian K-Theory

Abstract

This paper is devoted to classical Bott periodicity, its history and more recent extensions in algebraic and Hermitian K-theory. However, it does not aim at completeness. For instance, the variants of Bott periodicity related to bivariant K-theory are described by Cuntz in this handbook. As another example, we don't emphasize here the relation between motivic homotopy theory and Bott periodicity since it is also described by other authors of this handbook (Grayson, Kahn,. . .).