Knörrer periodicity and Bott periodicity
Copyright policy )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).
- University of Nebraska-Lincoln United States
- University of Nebraska System United States
Commutative Algebra (math.AC), K-theory, 510, Derived categories, triangulated categories, Topological \(K\)-theory, Knörrer periodicity, Enriched categories (over closed or monoidal categories), singularity theory, commutative algebra, FOS: Mathematics, Grothendieck groups, \(K\)-theory and commutative rings, Milnor fibration; relations with knot theory, matrix factorizations, Atiyah-Bott-Shapiro construction, K-Theory and Homology (math.KT), Mathematics - Commutative Algebra, Milnor fiber, Algebra, Mathematics - K-Theory and Homology, Geometry and Topology, Milnor fibration, Bott periodicity, triangulated categories, Mathematics
Commutative Algebra (math.AC), K-theory, 510, Derived categories, triangulated categories, Topological \(K\)-theory, Knörrer periodicity, Enriched categories (over closed or monoidal categories), singularity theory, commutative algebra, FOS: Mathematics, Grothendieck groups, \(K\)-theory and commutative rings, Milnor fibration; relations with knot theory, matrix factorizations, Atiyah-Bott-Shapiro construction, K-Theory and Homology (math.KT), Mathematics - Commutative Algebra, Milnor fiber, Algebra, Mathematics - K-Theory and Homology, Geometry and Topology, Milnor fibration, Bott periodicity, triangulated categories, Mathematics
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