{
  "id": "0711.2541",
  "version": "v14",
  "published": "2007-11-16T00:51:57.000Z",
  "updated": "2015-09-10T07:56:04.000Z",
  "title": "Schubert calculus and cohomology of Lie groups. Part I. 1-connected Lie groups",
  "authors": [
    "Haibao Duan",
    "Xuezhi Zhao"
  ],
  "comment": "32 pages; 4 tables",
  "categories": [
    "math.AT",
    "math.AG"
  ],
  "abstract": "Let $G$ be a compact and $1$--connected Lie group with a maximal torus $T$. Based on Schubert calculus on the flag manifold $G/T$ [15] we construct the integral cohomology ring $H^{\\ast}(G)$ uniformly for all $G$.",
  "revisions": [
    {
      "version": "v13",
      "updated": "2013-09-16T23:57:10.000Z",
      "title": "Schubert calculus and cohomology of Lie groups",
      "abstract": "Let G be a 1-connected simple Lie group with a maximal torus T. Combining the canonical presentation of the integral cohomology of the flag manifold G/T obtained in [20] with Leray-Serre spectral sequence of the fibration G\\toG/T, we construct the cohomology ring H^{\\ast}(G;F) uniformly for all G and F=Q,F_{p},Z.",
      "comment": "44 pages; 4 tables",
      "journal": null,
      "doi": null
    },
    {
      "version": "v14",
      "updated": "2015-09-10T07:56:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "55T10"
    ],
    "keywords": [
      "schubert calculus",
      "simple lie group",
      "flag manifold g/t",
      "leray-serre spectral sequence",
      "integral cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.2541D"
    }
  }
}