{
  "id": "1705.07610",
  "version": "v1",
  "published": "2017-05-22T08:41:43.000Z",
  "updated": "2017-05-22T08:41:43.000Z",
  "title": "Topological computation of some Stokes phenomena on the affine line",
  "authors": [
    "Andrea D'Agnolo",
    "Marco Hien",
    "Giovanni Morando",
    "Claude Sabbah"
  ],
  "comment": "51 pages",
  "categories": [
    "math.AG",
    "math.CA"
  ],
  "abstract": "Let $\\mathcal M$ be a holonomic algebraic $\\mathcal D$-module on the affine line, regular everywhere including at infinity. Malgrange gave a complete description of the Fourier-Laplace transform $\\widehat{\\mathcal M}$, including its Stokes multipliers at infinity, in terms of the quiver of $\\mathcal M$. Let $F$ be the perverse sheaf of holomorphic solutions to $\\mathcal M$. By the irregular Riemann-Hilbert correspondence, $\\widehat{\\mathcal M}$ is determined by the enhanced Fourier-Sato transform $F^\\curlywedge$ of $F$. Our aim here is to recover Malgrange's result in a purely topological way, by computing $F^\\curlywedge$ using Borel-Moore cycles. In this paper, we also consider some irregular $\\mathcal M$'s, like in the case of the Airy equation, where our cycles are related to steepest descent paths.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-22T08:41:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34M40",
      "44A10",
      "32C38"
    ],
    "keywords": [
      "affine line",
      "stokes phenomena",
      "topological computation",
      "steepest descent paths",
      "irregular riemann-hilbert correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}