{
  "id": "math/9812087",
  "version": "v3",
  "published": "1998-12-15T22:30:06.000Z",
  "updated": "1999-04-03T20:56:59.000Z",
  "title": "Cohomology rings and nilpotent quotients of real and complex arrangements",
  "authors": [
    "Daniel Matei",
    "Alexander I. Suciu"
  ],
  "comment": "LaTeX2e, 22 pages, to appear in Singularities and Arrangements, Sapporo-Tokyo 1998, Advanced Studies in Pure Mathematics",
  "journal": "Arrangements--Tokyo 1998, 185-215, Advanced Studies in Pure Mathematics, vol. 27, Kinokuniya, Tokyo, 2000",
  "categories": [
    "math.GT",
    "math.AG"
  ],
  "abstract": "For an arrangement with complement X and fundamental group G, we relate the truncated cohomology ring, H^{<=2}(X), to the second nilpotent quotient, G/G_3. We define invariants of G/G_3 by counting normal subgroups of a fixed prime index p, according to their abelianization. We show how to compute this distribution from the resonance varieties of the Orlik-Solomon algebra mod p. As an application, we establish the cohomology classification of 2-arrangements of n<=6 planes in R^4.",
  "revisions": [
    {
      "version": "v3",
      "updated": "1999-04-03T20:56:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B30",
      "57M05",
      "20F14",
      "20J05"
    ],
    "keywords": [
      "cohomology ring",
      "complex arrangements",
      "orlik-solomon algebra mod",
      "second nilpotent quotient",
      "cohomology classification"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....12087M"
    }
  }
}