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

@inproceedings{Mann2015BraneAC,
  title={Brane actions, categorifications of Gromov–Witten theory and quantum K–theory},
  author={Etienne Mann and Marco Robalo},
  year={2015}
}
  • Etienne Mann, Marco Robalo
  • Published 2015
  • Mathematics
  • 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. 

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    SHOWING 1-10 OF 43 REFERENCES

    Modular operads

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Quantum K -theory

    VIEW 8 EXCERPTS
    HIGHLY INFLUENTIAL

    Higher Algebra

    VIEW 9 EXCERPTS
    HIGHLY INFLUENTIAL

    In The moduli space of curves (Texel Island

    • Maxim Kontsevich. Enumeration of rational curves via tor actions
    • 1994), volume 129 of Progr. Math., pages 335–368. Birkhäuser Boston, Boston, MA,
    • 1995
    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    determinants of perfect complexes

    • T. Schürg, B. Toën, G. Vezzosi. Derived algebraic geometry
    • and applications to obstruction theories for maps and complexes. ArXiv e-prints, February
    • 2011
    VIEW 2 EXCERPTS
    HIGHLY INFLUENTIAL

    Adv

    • Marco Robalo. K-theory, the bridge from motives to noncommutative motives
    • Math., 269:399–550,
    • 2015
    VIEW 1 EXCERPT

    ArXiv e-prints

    • A. Brini, R. Cavalieri. Crepant resolutions, open strings
    • July
    • 2014
    VIEW 1 EXCERPT

    Math

    • Bertrand Toën. Derived algebraic geometry. EMS Surv
    • Sci., 1(2):153–245,
    • 2014