{
  "id": "math/9209219",
  "version": "v1",
  "published": "1992-09-01T00:00:00.000Z",
  "updated": "1992-09-01T00:00:00.000Z",
  "title": "Characteristic classes for $G$-structures",
  "authors": [
    "Dimitri Alekseevsky",
    "Peter W. Michor"
  ],
  "journal": "Diff. Geom. Appl. 3 (1993), 323-329",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $G\\subset GL(V)$ be a linear Lie group with Lie algebra $\\frak g$ and let $A(\\frak g)^G$ be the subalgebra of $G$-invariant elements of the associative supercommutative algebra $A(\\frak g)= S(\\frak g^*)\\otimes \\La(V^*)$. To any $G$-structure $\\pi:P\\to M$ with a connection $\\omega$ we associate a homomorphism $\\mu_\\omega:A(\\frak g)^G\\to \\Omega(M)$. The differential forms $\\mu_\\omega(f)$ for $f\\in A(\\frak g)^G$ which are associated to the $G$-structure $\\pi$ can be used to construct Lagrangians. If $\\omega$ has no torsion the differential forms $\\mu_\\omega(f)$ are closed and define characteristic classes of a $G$-structure. The induced homomorphism $\\mu'_\\omega:A(\\g)^G\\to H^*(M)$ does not depend on the choice of the torsionfree connection $\\omega$ and it is the natural generalization of the Chern Weil homomorphism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1992-09-01T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C10",
      "57R20"
    ],
    "keywords": [
      "differential forms",
      "linear lie group",
      "define characteristic classes",
      "natural generalization",
      "lie algebra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1992math......9219A"
    }
  }
}