{
  "id": "1104.1832",
  "version": "v3",
  "published": "2011-04-11T02:55:30.000Z",
  "updated": "2013-03-24T18:59:44.000Z",
  "title": "The cohomology ring of the GKM graph of a flag manifold of classical type",
  "authors": [
    "Yukiko Fukukawa",
    "Hiroaki Ishida",
    "Mikiya Masuda"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "If a closed smooth manifold $M$ with an action of a torus $T$ satisfies certain conditions, then a labeled graph $\\mG_M$ with labeling in $H^2(BT)$ is associated with $M$, which encodes a lot of geometrical information on $M$. For instance, the \"graph cohomology\" ring $\\mHT^*(\\mG_M)$ of $\\mG_M$ is defined to be a subring of $\\bigoplus_{v\\in V(\\mG_M)}H^*(BT)$, where $V(\\mG_M)$ is the set of vertices of $\\mG_M$, and is known to be often isomorphic to the equivariant cohomology $H^*_T(M)$ of $M$. In this paper, we determine the ring structure of $\\mHT^*(\\mG_M)$ with $\\Z$ (resp. $\\Z[1/2]$) coefficients when $M$ is a flag manifold of type A, B or D (resp. C) in an elementary way.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-03-24T18:59:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "55N91"
    ],
    "keywords": [
      "flag manifold",
      "gkm graph",
      "classical type",
      "cohomology ring",
      "closed smooth manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.1832F"
    }
  }
}