{
  "id": "math/0412057",
  "version": "v2",
  "published": "2004-12-02T17:02:33.000Z",
  "updated": "2005-08-18T20:02:22.000Z",
  "title": "Conjugation spaces",
  "authors": [
    "Jean-Claude Hausmann",
    "Tara Holm",
    "Volker Puppe"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-39.abs.html",
  "journal": "Algebr. Geom. Topol. 5 (2005) 923-964",
  "categories": [
    "math.AT",
    "math.SG"
  ],
  "abstract": "There are classical examples of spaces X with an involution tau whose mod 2-comhomology ring resembles that of their fixed point set X^tau: there is a ring isomorphism kappa: H^2*(X) --> H^*(X^tau). Such examples include complex Grassmannians, toric manifolds, polygon spaces. In this paper, we show that the ring isomorphism kappa is part of an interesting structure in equivariant cohomology called an H^*-frame. An H^*-frame, if it exists, is natural and unique. A space with involution admitting an H^*-frame is called a conjugation space. Many examples of conjugation spaces are constructed, for instance by successive adjunctions of cells homeomorphic to a disk in C^k with the complex conjugation. A compact symplectic manifold, with an anti-symplectic involution compatible with a Hamiltonian action of a torus T, is a conjugation space, provided X^T is itself a conjugation space. This includes the co-adjoint orbits of any semi-simple compact Lie group, equipped with the Chevalley involution. We also study conjugate-equivariant complex vector bundles (`real bundles' in the sense of Atiyah) over a conjugation space and show that the isomorphism kappa maps the Chern classes onto the Stiefel-Whitney classes of the fixed bundle.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-08-18T20:02:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N91",
      "55M35",
      "53D05",
      "57R22"
    ],
    "keywords": [
      "conjugation space",
      "study conjugate-equivariant complex vector bundles",
      "ring isomorphism kappa",
      "semi-simple compact lie group",
      "involution"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}