The holonomic-module model conjecture for the Fukaya category
The holonomic-module model conjecture for the Fukaya category
Let be a symplectic manifold, let denote its naive Fukaya category, and let be the derived -category of holonomic modules over the quantized algebra of smooth functions on . For Lagrangian submanifolds and holonomic modules , suppose that the kernels and the higher compositions are chosen as described in the preceding construction. Holonomic-module model conjecture. (i) The higher compositions , for , give rise to a structure of an -category on . (ii) This category is -equivalent to , with . This conjecture proposes an algebraic replacement of instanton counting in the Fukaya category by homomorphisms between holonomic modules and local systems supported on Lagrangian submanifolds; the source does not state whether it has been resolved.
Sources & referencesView supporting material
Primary source
Paul Bressler and Yan Soibelman, “Mirror symmetry and deformation quantization”, arXiv:hep-th/0202128 (2002).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.