Fukaya's Witten-complex conjecture for Lagrangian disc instantons
Fukaya's Witten-complex conjecture for Lagrangian disc instantons
Let be a manifold, let be functions on , and let for . For intersection points , let be a linear combination of eigenfunctions with sufficiently small eigenvalues of the Witten Laplacian on -forms associated with , localized around . Fukaya's conjecture. The pairing of these Witten-complex states should satisfy
where the sum is over pseudoholomorphic triangles, or disc instantons, with vertices . This is the simplest expected form of an -category structure on Witten complexes associated with different Morse functions, relating their products to Fukaya-type disc instantons.
Sources & referencesView supporting material
Primary source
Alexander Getmanenko, “Resurgent Analysis of the Witten Laplacian in One Dimension”, arXiv:0809.0441 (2010).
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