The quantum connection, Fourier-Laplace transform, and families of A-infinity-categories
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 unr...
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Zusammenfassung: | 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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DOI: | 10.48550/arxiv.2308.13567 |