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arXiv · 1505.02964

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

Etienne Mann·Marco Robalo
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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.

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Etienne Mann, Marco Robalo. 2017-06-18. Brane actions, Categorification of Gromov-Witten theory and Quantum K-theory. https://doi.org/10.2140/gt.2018.22.1759

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