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arXiv · 2308.13567

The quantum connection, Fourier-Laplace transform, and families of A-infinity-categories

Daniel Pomerleano·Paul Seidel
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Abstract

Take a closed monotone symplectic manifold containing a smooth anticanonical divisor. The quantum connection on its cohomology has singularities at zero and infinity (in the quantum parameter). At zero it has a regular singular point, by definition. We show that the singularity at infinity is of unramified exponential type. The argument involves: realizing cohomology as a deformation of the symplectic cohomology of the divisor complement; the corresponding deformation of the wrapped Fukaya category; a new categorical interpretation of the Fourier-Laplace transform of D-modules; and the regularity theorem of Petrov-Vaintrob-Vologodsky in noncommutative geometry.

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Daniel Pomerleano, Paul Seidel. 2023-08-25. The quantum connection, Fourier-Laplace transform, and families of A-infinity-categories. https://arxiv.org/abs/2308.13567

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