Mirror symmetry and noncommutative geometry of A∞-categories

@article{Soibelman2004MirrorSA,
  title={Mirror symmetry and noncommutative geometry of A∞-categories},
  author={Y. Soibelman},
  journal={Journal of Mathematical Physics},
  year={2004},
  volume={45},
  pages={3742-3757}
}
  • Y. Soibelman
  • Published 2004
  • Mathematics
  • Journal of Mathematical Physics
  • Homological mirror symmetry aims to explain the phenomenon of mirror symmetry in the language of A∞-categories and their deformation theory. In these notes I discuss various aspects of this approach from the point of view of noncommutative algebraic geometry in the tensor category of graded vector spaces. 
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    References

    SHOWING 1-10 OF 24 REFERENCES
    Quantum Tori, Mirror Symmetry and Deformation Theory
    • 37
    • PDF
    Mirror symmetry and algebraic geometry
    • 857
    • PDF
    Mirror symmetry is T duality
    • 1,159
    • PDF
    Mirror symmetry and deformation quantization
    • 27
    • PDF
    Mirror Manifolds And Topological Field Theory
    • 409
    • PDF
    Homological Algebra of Mirror Symmetry
    • 1,123
    • PDF
    Homological mirror symmetry and torus fibrations
    • 484
    • PDF
    Remarks on A-branes, mirror symmetry, and the Fukaya category
    • 167
    • PDF