{
  "id": "2105.13107",
  "version": "v1",
  "published": "2021-05-27T13:04:57.000Z",
  "updated": "2021-05-27T13:04:57.000Z",
  "title": "${\\mathcal C}^{\\infty}$-equivalence of analytic branches in $({\\mathbb C}^3,0)$",
  "authors": [
    "Pedro Fortuny Ayuso"
  ],
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "We prove that two analytic branches in $(\\mathbb{C}^3,0)$ admit an ambient smooth isotopy if and only if their resolutions of singularities have the same dual graph. Thus, the dual graph is a smooth invariant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-27T13:04:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S15",
      "14B05",
      "14H20",
      "14H50"
    ],
    "keywords": [
      "analytic branches",
      "equivalence",
      "dual graph",
      "ambient smooth isotopy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}