{
  "id": "1701.03631",
  "version": "v1",
  "published": "2017-01-13T11:27:42.000Z",
  "updated": "2017-01-13T11:27:42.000Z",
  "title": "Braid groups in handlebodies and corresponding Hecke algebras",
  "authors": [
    "Valetiy G. Bardakov"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "In this paper we study the kernel of the homomorphism $B_{g,n} \\to B_n$ of the braid group $B_{g,n}$ in the handlebody $\\mathcal{H}_g$ to the braid group $B_n$. We prove that this kernel is a semi-direct product of free groups. Also, we introduce an algebra $H_{g,n}(q)$, which is some analog of the Hecke algebra $H_n(q)$, constructed by the braid group $B_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-13T11:27:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20E05"
    ],
    "keywords": [
      "braid group",
      "corresponding hecke algebras",
      "handlebody",
      "free groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}