{
  "id": "math/0008235",
  "version": "v1",
  "published": "2000-08-31T14:19:07.000Z",
  "updated": "2000-08-31T14:19:07.000Z",
  "title": "Braid structures in knot complements, handlebodies and 3-manifolds",
  "authors": [
    "Sofia Lambropoulou"
  ],
  "comment": "16 pages, 4 figures, to appear in the proceedings of Knots in Hellas '98, Series of Knots and Everything, Vol. 24, World Scientific",
  "journal": "{\\it Proceedings of Knots in Hellas '98}, World Scientific Press, Series of Knots and Everything {\\bf 24}, 274--289 (2000).",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "We consider braids on $m+n$ strands, such that the first $m$ strands are trivially fixed. We denote the set of all such braids by $B_{m,n}$. Via concatenation $B_{m,n}$ acquires a group structure. The objective of this paper is to find a presentation for $B_{m,n}$ using the structure of its corresponding pure braid subgroup, $P_{m,n}$, and the fact that it is a subgroup of the classical Artin group $B_{m+n}$. Then we give an irredundant presentation for $B_{m,n}$. The paper concludes by showing that these braid groups or appropriate cosets of them are related to knots in handlebodies, in knot complements and in c.c.o. 3--manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-08-31T14:19:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "knot complements",
      "braid structures",
      "handlebodies",
      "corresponding pure braid subgroup",
      "group structure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......8235L"
    }
  }
}