{
  "id": "1702.05707",
  "version": "v1",
  "published": "2017-02-19T06:47:02.000Z",
  "updated": "2017-02-19T06:47:02.000Z",
  "title": "Generators for a complex hyperbolic braid group",
  "authors": [
    "Daniel Allcock",
    "Tathagata Basak"
  ],
  "comment": "46 pages, 7 figures, submitted",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give generators for a certain complex hyperbolic braid group. That is, we remove a hyperplane arrangement from complex hyperbolic $13$-space, take the quotient of the remaining space by a discrete group, and find generators for the orbifold fundamental group of the quotient. These generators have the most natural form: loops corresponding to the hyperplanes which come nearest the basepoint. Our results support the conjecture that motivated this study, the \"monstrous proposal\", which posits a relationship between this braid group and the monster finite simple group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-19T06:47:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M05",
      "20F36",
      "52C35",
      "32S22"
    ],
    "keywords": [
      "complex hyperbolic braid group",
      "generators",
      "monster finite simple group",
      "orbifold fundamental group",
      "discrete group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}