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

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arxiv 2308.13567 v5 pith:N6R22JTW submitted 2023-08-25 math.SG math.AG

Daniel Pomerleano , Paul Seidel This is my paper · ORCID
classification math.SGmath.AG
keywords cohomologyquantumconnectiondeformationdivisorfourier-laplaceinfinitysymplectic
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Noncommutative Cartier Formulae

    math.AT 2026-07 conditional novelty 8.0 of 10

    A noncommutative Cartier formula for E1-ring spectra is proven and applied to show that p-curvature of the quantum connection computes quantum Steenrod operations for Calabi-Yau symplectic manifolds.

  2. The Getzler-Gauss-Manin connection and Kontsevich-Soibelman operations on the periodic cyclic homology

    math.QA 2026-01 conditional novelty 8.0 of 10

    Over a field of characteristic p, all Kontsevich-Soibelman operations on periodic cyclic homology are generated by the p-fold equivariant cap product and commute with the Getzler-Gauss-Manin connection.

  3. The cubic threefold is symplectically irrational

    math.SG 2026-08 conditional novelty 6.0 of 10

    The cubic threefold is symplectically irrational, proved via the formal monodromy of its quantum connection.

  4. The quantum connection and its mod p reduction

    math.SG 2026-06 unverdicted novelty 6.0 of 10

    Refines mod p approaches to the quantum connection for monotone symplectic manifolds and strengthens its relation to quantum Steenrod operations for more precise singularity information.

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