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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Brane actions, categorifications of Gromov–Witten theory and quantum K–theory

Etienne Mann and Marco Robalo

Geometry & Topology 22 (2018) 1759–1836
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