## Quantum $$K$$-theory. I: Foundations.(English)Zbl 1051.14064

The author studies the foundations of quantum $$K$$-theory, a $$K$$-theoretic version of quantum cohomology theory, giving 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. As a result, he develops a new class of Frobenius manifolds, and answers an open question of A. Bayer and Y. I. Manin [http://arxiv.org/abs/math.AG/0103164].

### MSC:

 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) 19E08 $$K$$-theory of schemes 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds 55N15 Topological $$K$$-theory

quantum K-theory
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### References:

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