{
  "id": "math/0507451",
  "version": "v1",
  "published": "2005-07-21T20:26:48.000Z",
  "updated": "2005-07-21T20:26:48.000Z",
  "title": "Algebraic cycles and the classical groups II: Quaternionic cycles",
  "authors": [
    "H Blaine Lawson Jr",
    "Paulo Lima-Filho",
    "Marie-Louise Michelsohn"
  ],
  "comment": "Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper27.abs.html",
  "journal": "Geom. Topol. 9(2005) 1187-1220",
  "categories": [
    "math.AT",
    "math.AG"
  ],
  "abstract": "In part I of this work we studied the spaces of real algebraic cycles on a complex projective space P(V), where V carries a real structure, and completely determined their homotopy type. We also extended some functors in K-theory to algebraic cycles, establishing a direct relationship to characteristic classes for the classical groups, specially Stiefel-Whitney classes. In this sequel, we establish corresponding results in the case where V has a quaternionic structure. The determination of the homotopy type of quaternionic algebraic cycles is more involved than in the real case, but has a similarly simple description. The stabilized space of quaternionic algebraic cycles admits a nontrivial infinite loop space structure yielding, in particular, a delooping of the total Pontrjagin class map. This stabilized space is directly related to an extended notion of quaternionic spaces and bundles (KH-theory), in analogy with Atiyah's real spaces and KR-theory, and the characteristic classes that we introduce for these objects are nontrivial. The paper ends with various examples and applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-21T20:26:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C25",
      "55P43",
      "14P99",
      "19L99",
      "55P47",
      "55P91"
    ],
    "keywords": [
      "classical groups",
      "quaternionic cycles",
      "loop space structure yielding",
      "nontrivial infinite loop space structure",
      "characteristic classes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}