{
  "id": "2203.03239",
  "version": "v1",
  "published": "2022-03-07T09:53:18.000Z",
  "updated": "2022-03-07T09:53:18.000Z",
  "title": "Twisted Iwasawa invariants of knots",
  "authors": [
    "Ryoto Tange",
    "Jun Ueki"
  ],
  "comment": "17 pages, 1 figure",
  "categories": [
    "math.GT",
    "math.NT"
  ],
  "abstract": "Let $p$ be a prime number and $m$ an integer coprime to $p$. In the spirit of arithmetic topology, we introduce the notions of the twisted Iwasawa invariants $\\lambda, \\mu, \\nu$ of ${\\rm GL}_N$-representations and $\\mathbb{Z}/m\\mathbb{Z}\\times \\mathbb{Z}_p$-covers of knots. We prove among other things that the set of Iwasawa invariants determine the genus and the fiberedness of a knot, yielding their profinite rigidity. Several intuitive examples are attached. We further prove the $\\mu=0$ theorem for ${\\rm SL}_2$-representations of twist knot groups and give some remarks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-07T09:53:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "11R23",
      "57M10",
      "11S99"
    ],
    "keywords": [
      "twisted iwasawa invariants",
      "iwasawa invariants determine",
      "twist knot groups",
      "representations",
      "prime number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}