Quantum $K$-theory, I: Foundations

By Y.-P. Lee. 2001

172 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/79f7d0ad60cde58ed3a5ac55bfcbd314d96be766

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In Geometry and Topology

1. Valentin Tonita
2. Alexander Givental
3. H. Iritani
4. A. Okounkov
5. C. Teleman
6. T. Milanov
7. Hsian-Hua Tseng
8. E. Getzler

In Mathematical Physics

1. Valentin Tonita
2. Alexander Givental
3. A. Okounkov
4. T. Milanov
5. C. Teleman
6. H. Iritani
7. Hsian-Hua Tseng
8. E. Getzler

Citations in the corpus

• The Hirzebruch--Riemann--Roch theorem in true genus-0 quantum K-theory (2011, methodology): “According to [20], the collection of virtual structure sheaves on the spaces M X,d g,n satisfies K-theoretic counterparts of Kontsevich–Manin’s axioms [19] for Gromov–Witten invariants.”