{
  "id": "1812.09413",
  "version": "v1",
  "published": "2018-12-21T23:34:29.000Z",
  "updated": "2018-12-21T23:34:29.000Z",
  "title": "Algorithmic aspects of immersibility and embeddability",
  "authors": [
    "Fedor Manin",
    "Shmuel Weinberger"
  ],
  "comment": "15 pages; comments welcome!",
  "categories": [
    "math.GT",
    "cs.CG"
  ],
  "abstract": "We analyze an algorithmic question about immersion theory: for which $m$, $n$, and $CAT=\\mathbf{Diff}$ or $\\mathbf{PL}$ is the question of whether an $m$-dimensional $CAT$-manifold is immersible in $\\mathbb{R}^n$ decidable? As a corollary, we show that the smooth embeddability of an $m$-manifold with boundary in $\\mathbb{R}^n$ is undecidable when $n-m$ is even and $11m \\geq 10n+1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-21T23:34:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R42",
      "57Q35",
      "03D15"
    ],
    "keywords": [
      "algorithmic aspects",
      "immersibility",
      "algorithmic question",
      "immersion theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}