On the WDVV equation in quantum K-theory.

By Alexander Givental. 2000

127 citations recorded by the source corpus.

0. Introduction. Quantum cohomology theory can be described in general words as intersection theory in spaces of holomorphic curves in a given Kahler or almost Kahler manifold X. By quantum K-theory we may similarly understand a study of complex vector bundles over the spaces of holomorphic curves in X. In these notes, we will introduce a K-theoretic version of the Witten-Dijkgraaf-Verlinde-Verlinde equation which expresses the associativity constraint of the “quantum multiplication” operation on K(X). Intersection indices of cohomology theory, ∫

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e651783dbf88119f73803161a36566a83a67e2d3

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Citations in the corpus

The structure of 2D semi-simple field theories (2007, background): “The divisor equation (see for instance [13, 23]) ∫ GWn+1 δ (.”
Lectures on K-theoretic computations in enumerative geometry (2015, background): “In K-theoretic GW computations, there is a correction to gluing, discovered in [36] and discussed in detail in [49].”
Symplectic geometry of Frobenius structures (2003, methodology): “As it was found in [22], K-theoretic genus 0 Gromov – Witten invariants define a “Frobenius-like” structure on K which however exhibits the following remarkable distinction from the case of cohomology theory.”
The Hirzebruch--Riemann--Roch theorem in true genus-0 quantum K-theory (2011, methodology): “They were first introduced in [10] (albeit, in a limited generality of genus-0 curves mapped to homogeneous Kähler spaces), where it was shown that such invariants define”
QUANTUM K-THEORY OF GRASSMANNIANS (2008, unknown): “A G ] 1 3 Ju n 20 09”
Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups (2001, background): “Let L denote the universal cotangent line bundle over X1,d formed by the cotangent lines T ∗ εΣ to the curves (Σ, ε) at the marked point ε (see [11] for a discussion of these line bundles in the context of K-theory).”
Finiteness of cominuscule quantum K-theory (2010, unknown): “A G ] 1 5 Ju n 20 12”
A Chevalley formula for the equivariant quantum $K$-theory of cominuscule varieties (2016, background): “A theorem of Givental states that this defines an associative product [26] (see also [64, 60, 42, 46]).”