{
  "id": "1508.02430",
  "version": "v1",
  "published": "2015-08-10T21:19:00.000Z",
  "updated": "2015-08-10T21:19:00.000Z",
  "title": "Algebraic structures on cohomology of configuration spaces of manifolds with flows",
  "authors": [
    "Jordan S. Ellenberg",
    "John D. Wiltshire-Gordon"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "math.AT",
    "math.CO",
    "math.RT"
  ],
  "abstract": "Let PConf^n M be the configuration space of ordered n-tuples of distinct points on a smooth manifold M admitting a nowhere-vanishing vector field. We show that the ith cohomology group with coefficients in a field H^i(PConf^n M, k) is an N-module, where N is the category of noncommutative finite sets introduced by Pirashvili and Richter. Studying the representation theory of N, we obtain new polynomiality results for the cohomology groups H^i(PConf^n M, k). In the case of unordered configuration space Conf^n M = (PConf^n M)/S_n and rational coefficients, we show that cohomology dimension in fixed degree is nondecreasing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-10T21:19:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R80",
      "20J99",
      "20C15"
    ],
    "keywords": [
      "configuration space",
      "algebraic structures",
      "ith cohomology group",
      "distinct points",
      "polynomiality results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150802430E"
    }
  }
}