Knörrer Periodicity and Bott Periodicity

The goal of this article is to explain a precise sense in which Knörrer periodicity in commutative algebra and Bott periodicity in topological $K$-theory are compatible phenomena. Along the way, we prove an 8-periodic version of Knörrer 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).

2010 Mathematics Subject Classification: 13D15, 18D20, 18E30, 32S55, 55N15

Keywords and Phrases: Atiyah-Bott-Shapiro construction, Bott periodicity, Knörrer periodicity, matrix factorizations, Milnor fibration

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