{
  "id": "2305.18697",
  "version": "v1",
  "published": "2023-05-30T02:42:14.000Z",
  "updated": "2023-05-30T02:42:14.000Z",
  "title": "A braid monodromy presentation for the pure braid group",
  "authors": [
    "So Yamagata"
  ],
  "comment": "26 pages, 42 figures",
  "categories": [
    "math.GT",
    "math.CO",
    "math.GR"
  ],
  "abstract": "In the present paper, we consider a ``lexicographic section'' of the braid arrangement, and give a presentation of the fundamental group of its complement using the braid monodromy technique. We show that the resulting presentation coincides with the modified Artin presentation given by Margalit--McCammond. Moreover, we generalize the construction to the Manin--Schechtman arrangement $MS(n,k)$, a generalization of the braid arrangement. In particular, we give a presentation of $\\pi_1(\\mathbb{C}^5 \\setminus MS(5,2))$, which is the simplest and nontrivial example of the Manin--Schechtman arrangements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-30T02:42:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20F05",
      "57K20",
      "14H30"
    ],
    "keywords": [
      "pure braid group",
      "braid monodromy presentation",
      "manin-schechtman arrangement",
      "braid arrangement",
      "braid monodromy technique"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}