Brane actions, categorifications of Gromov–Witten theory and quantum K–theory

Mann, Etienne; Robalo, Marco

doi:10.2140/gt.2018.22.1759

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Brane actions, categorifications of Gromov–Witten theory and quantum K–theory

Etienne Mann and Marco Robalo

Geometry & Topology 22 (2018) 1759–1836

DOI: 10.2140/gt.2018.22.1759

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 and Lee.

Keywords

Gromov–Witten theory, higher category, derived algebraic geometry

Mathematical Subject Classification 2010

Primary: 14N35

References

Publication

Received: 7 December 2016

Revised: 4 April 2017

Accepted: 13 June 2017

Published: 16 March 2018

Proposed: Richard Thomas

Seconded: Jim Bryan, Peter Teichner

Authors

Etienne Mann
LAREMA UMR - 6093 Département de Mathématiques Bâtiment I Faculté des Sciences 2 Université d’Angers Angers France

Marco Robalo
Sorbonne Université Faculté des Sciences et Ingénierie Institut de Mathématiques de Jussieu-PRG Paris France

Volume 22, issue 3 (2018)