Skip to Main content Skip to Navigation
Journal articles

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.
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01151061
Contributor : Etienne Mann <>
Submitted on : Friday, December 1, 2017 - 9:58:58 AM
Last modification on : Saturday, April 11, 2020 - 2:03:14 AM

File

finalversionGT-GW.pdf
Files produced by the author(s)

Identifiers

Citation

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⟩

Share

Metrics

Record views

423

Files downloads

429