{
  "id": "1910.00712",
  "version": "v1",
  "published": "2019-10-01T23:27:05.000Z",
  "updated": "2019-10-01T23:27:05.000Z",
  "title": "Homomorphisms between braid groups",
  "authors": [
    "Lei Chen",
    "Kevin Kordek",
    "Dan Margalit"
  ],
  "comment": "33 pages, 3 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give a complete classification of homomorphisms from the braid group on $n$ strands to the braid group on $2n$ strands when $n$ is at least 5. We also classify endomorphisms of the braid group on 4 stands. Our classifications suggest a recursive classification of homomorphisms between any braid groups. We also give a simple, geometric proof of a theorem of Lin that highly constrains the holomorphic maps that may exist between spaces of monic, square-free polynomials of a given degree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-01T23:27:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "braid group",
      "homomorphisms",
      "square-free polynomials",
      "complete classification",
      "holomorphic maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}