English

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

Algebraic Geometry 2018-03-28 v2 Algebraic Topology Category Theory K-Theory and Homology

Abstract

Let X be a smooth projective variety. Using the idea of brane actions discovered by To\"en, 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.

Keywords

Cite

@article{arxiv.1505.02964,
  title  = {Brane actions, Categorification of Gromov-Witten theory and Quantum K-theory},
  author = {Etienne Mann and Marco Robalo},
  journal= {arXiv preprint arXiv:1505.02964},
  year   = {2018}
}

Comments

final version, 64 pages, accepted for publication in Geometry & Topology