Brane actions, Categorification of Gromov-Witten theory and Quantum K-theory

Abstract

Let X be a smooth projective variety. Using the idea of brane actions discovered by Toën, we construct a lax associative action of the operad of stable curves of genus zero on the variety X seen as an object in correspondences in derived stacks. This action encodes the Gromov-Witten theory of X in purely geometrical terms and induces an action on the derived category Qcoh(X) which allows us to recover the Quantum K-theory of Givental-Lee.

final version, 64 pages, accepted for publication in Geometry & Topology

References in corpus (1)

• Perfect complexes on algebraic stacks

Cited by in corpus (4)

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