{
  "id": "2401.01847",
  "version": "v1",
  "published": "2024-01-03T17:38:31.000Z",
  "updated": "2024-01-03T17:38:31.000Z",
  "title": "Horizontal Goodman surgery and almost equivalence of pseudo-Anosov flows",
  "authors": [
    "Chi Cheuk Tsang"
  ],
  "comment": "71 pages, 35 figures",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "We provide an exposition of a `horizontal' generalization of Goodman's surgery operation on (pseudo-)Anosov flows. This operation is performed by cutting along a specific kind of annulus that is transverse to the flow and regluing with a Dehn twist of the appropriate sign. We then show that performing horizontal Goodman surgery on a transitive pseudo-Anosov flow yields an almost equivalent flow, i.e. the original flow and the surgered flow are orbit equivalent after drilling out a finite collection of closed orbits. We obtain some almost equivalence results by applying this theorem on examples of the surgery operation. Along the way, we also show a structural stability result for pseudo-Anosov flows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-03T17:38:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equivalence",
      "transitive pseudo-anosov flow yields",
      "structural stability result",
      "performing horizontal goodman surgery",
      "goodmans surgery operation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 71,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}