Knoerrer Periodicity and Bott Periodicity
Michael K. Brown

TL;DR
This paper explores the connection between Knoerrer periodicity in algebra and Bott periodicity in topology, establishing an 8-periodic version for real hypersurface singularities and linking algebraic invariants to topological K-theory.
Contribution
It introduces an 8-periodic version of Knoerrer periodicity for real hypersurface singularities and constructs a homomorphism connecting algebraic and topological K-theory.
Findings
Proves 8-periodic Knoerrer periodicity for real hypersurface singularities
Constructs a homomorphism from matrix factorizations to topological K-theory
Establishes compatibility between algebraic and topological periodicities
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 into the topological K-theory of its Milnor fiber (positive or negative Milnor fiber).
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Taxonomy
TopicsEngineering and Materials Science Studies
