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Quantum K-Theory I: Foundations

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arxiv math/0105014 v4 pith:Y37X5UDV submitted 2001-05-02 math.AG math.KT

Y.-P. Lee This is my paper · ORCID
classification math.AGmath.KT
keywords quantumcohomologyfoundationsgivesk-theoryordinaryanalogousclass
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This work is devoted to the study of the foundations of quantum K-theory, a K-theoretic version of quantum cohomology theory. In particular, it gives a deformation of the ordinary K-ring K(X) of a smooth projective variety X, analogous to the relation between quantum cohomology and ordinary cohomology. This new quantum product also gives a new class of Frobenius manifolds.

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  1. Quantum K-theory levels in physics and math

    hep-th 2025-06 conditional novelty 6.0 of 10

    Chern-Simons levels and Ruan-Zhang levels are identified as the same twisting of quantum K-theory, with Coulomb branch equations matching difference operator symbols and geometric windows matching mirror triviality.

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