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Brane actions, categorifications 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 formulas for Quantum K-theory of Givental-Lee. This paper is the first step of a larger project. We believe that this action in correspondences encodes the full classical cohomological Gromov-Witten invariants of X. This will appear in a second paper.
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Contributor : Etienne Mann <>
Submitted on : Friday, December 1, 2017 - 9:58:58 AM
Last modification on : Monday, December 14, 2020 - 5:28:34 PM


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Etienne Mann, Marco Robalo. Brane actions, categorifications of Gromov–Witten theory and quantum K–theory. Geometry and Topology, Mathematical Sciences Publishers, 2018, 22 (3), pp.1759-1836. ⟨10.2140/gt.2018.22.1759⟩. ⟨hal-01151061v2⟩



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