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<p>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 <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mi>D</mi> </math></EquationSource> <EquationSource Format="TEX">$D$</EquationSource> </InlineEquation>-modules; and the regularity theorem of Petrov-Vaintrob-Vologodsky in noncommutative geometry.</p>

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The quantum connection, Fourier-Laplace transform, and families of \(A_{\infty }\)-categories

  • 期刊论文

  • 发表日期：

    2026年7月7日

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  • D. Pomerleano,
  • P. Seidel

摘要

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 $D$ -modules; and the regularity theorem of Petrov-Vaintrob-Vologodsky in noncommutative geometry.