{
  "id": "2403.12492",
  "version": "v1",
  "published": "2024-03-19T07:00:51.000Z",
  "updated": "2024-03-19T07:00:51.000Z",
  "title": "A prime decomposition theorem for string links in a thickened surface",
  "authors": [
    "Vladimir Tarkaev"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove a prime decomposition theorem for string links in a thickened surface. Namely, we prove that any non-braid string link $\\ell \\subset \\Sigma \\times I$, where $\\Sigma$ is a compact orientable (not necessarily closed) surface other than $S^2$, can be written in the form $\\ell =\\ell_1 \\# \\ldots \\# \\ell_m$, where $\\ell_j,j=1,\\ldots,m,$ is prime string link defined up to braid-equivalence, and the decomposition is unique up to permuting the order of factors in its right-hand side.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-19T07:00:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "prime decomposition theorem",
      "thickened surface",
      "prime string link",
      "non-braid string link",
      "right-hand side"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}