{
  "id": "1701.07768",
  "version": "v1",
  "published": "2017-01-26T16:44:39.000Z",
  "updated": "2017-01-26T16:44:39.000Z",
  "title": "Cup products, lower central series, and holonomy Lie algebras",
  "authors": [
    "Alexander I. Suciu",
    "He Wang"
  ],
  "comment": "26 pages. arXiv admin note: substantial text overlap with arXiv:1504.08294",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We generalize basic results relating the associated graded Lie algebra and the holonomy Lie algebra from finitely presented, commutator-relators groups to arbitrary finitely presented groups. In the process, we give an explicit formula for the cup-product in the cohomology of a finite 2-complex, and an algorithm for computing the corresponding holonomy Lie algebra, using a Magnus expansion method. We illustrate our approach with examples drawn from a variety of group-theoretic and topological contexts, such as link groups, one-relator groups, and fundamental groups of Seifert fibered manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-26T16:44:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F40",
      "57M05",
      "17B70",
      "20F14",
      "20J05"
    ],
    "keywords": [
      "lower central series",
      "cup products",
      "corresponding holonomy lie algebra",
      "magnus expansion method",
      "explicit formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}