{
  "id": "0906.3494",
  "version": "v2",
  "published": "2009-06-18T18:10:17.000Z",
  "updated": "2010-10-26T20:51:50.000Z",
  "title": "The third order helicity of magnetic fields via link maps II",
  "authors": [
    "R. Komendarczyk"
  ],
  "comment": "19 pages, 2 figures; published version",
  "categories": [
    "math.DS",
    "math-ph",
    "math.DG",
    "math.GT",
    "math.MP"
  ],
  "abstract": "In this sequel we extend the derivation of the third order helicity to magnetic fields supported on unlinked domains in 3-space. The formula is expressed in terms of generators of the deRham cohomology of the configuration space of three points in $\\R^3$, which is a more practical domain from the perspective of applications. It also admits an ergodic interpretation as an average asymptotic Milnor $\\bar{\\mu}_{123}$-invariant and allows us to obtain the $L^2$-energy bound for the magnetic field. As an intermediate step we derive an integral formula for Milnor $\\bar{\\mu}_{123}$-invariant for parametrized Borromean links in $\\R^3$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-26T20:51:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76W05",
      "57M25",
      "58F18",
      "58A10",
      "05.20.-y",
      "04.20.Gz"
    ],
    "keywords": [
      "third order helicity",
      "magnetic field",
      "link maps",
      "average asymptotic milnor",
      "parametrized borromean links"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.3516611",
      "journal": "Journal of Mathematical Physics",
      "year": 2010,
      "month": "Dec",
      "volume": 51,
      "number": 12,
      "pages": 2702
    },
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JMP....51l2702K"
    }
  }
}