Knoerrer Periodicity and Bott Periodicity

Abstract

The goal of this article is to explain a precise sense in which Knoerrer periodicity in commutative algebra and Bott periodicity in topological K-theory are compatible phenomena. Along the way, we prove an 8-periodic version of Knoerrer periodicity for real isolated hypersurface singularities, and we construct a homomorphism from the Grothendieck group of the homotopy category of matrix factorizations of a complex (real) polynomial $f$ into the topological K-theory of its Milnor fiber (positive or negative Milnor fiber).