The quantum connection, Fourier-Laplace transform, and families of A-infinity-categories
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| _version_ | 1866912000289800192 |
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| author | Pomerleano, Daniel Seidel, Paul |
| author_facet | Pomerleano, Daniel Seidel, Paul |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_13567 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The quantum connection, Fourier-Laplace transform, and families of A-infinity-categories Pomerleano, Daniel Seidel, Paul Symplectic Geometry Algebraic Geometry 53D40 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. |
| title | The quantum connection, Fourier-Laplace transform, and families of A-infinity-categories |
| topic | Symplectic Geometry Algebraic Geometry 53D40 |
| url | https://arxiv.org/abs/2308.13567 |