{
  "id": "math/0405307",
  "version": "v1",
  "published": "2004-05-15T12:42:31.000Z",
  "updated": "2004-05-15T12:42:31.000Z",
  "title": "On the cohomology of Artin groups in local systems and the associated Milnor fiber",
  "authors": [
    "Filippo Callegaro"
  ],
  "comment": "9 pages",
  "journal": "J. Pure Appl. Algebra 197 (2005), no. 1-3, 323--332",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let W be a finite irreducible Coxeter group and let X_W be the classifying space for G_W, the associated Artin group. If A is a commutative unitary ring, we consider the two local systems L_q and L_q' over X_W, respectively over the modules A[q,q^{-1}] and A[[q,q^{-1}]], given by sending each standard generator of G_W into the automorphism given by the multiplication by q. We show that H^*(X_W,L_q') = H^{*+1}(X_W,L_q) and we generalize this relation to a particular class of algebraic complexes. We remark that H^*(X_W,L_q') is equal to the cohomology with trivial coefficients A of the Milnor fiber of the discriminant bundle of the associated reflection group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-15T12:42:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20J06",
      "32S55"
    ],
    "keywords": [
      "associated milnor fiber",
      "local systems",
      "cohomology",
      "finite irreducible coxeter group",
      "discriminant bundle"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5307C"
    }
  }
}