{
  "id": "math/0608266",
  "version": "v4",
  "published": "2006-08-10T21:09:06.000Z",
  "updated": "2008-12-31T18:02:15.000Z",
  "title": "Vector bundles and Gromov-Hausdorff distance",
  "authors": [
    "Marc A. Rieffel"
  ],
  "comment": "66 pages; revised to reflect the new paper arXiv:0810.4695 of Hanfeng Li, which answers a question in my previous versions, and shows how to get better estimates in a number of my theorems. Also, a few small improvements elsewhere",
  "journal": "Journal of K-Theory, 5 (2010), 39-103",
  "categories": [
    "math.MG",
    "math.OA"
  ],
  "abstract": "We show how to make precise the vague idea that for compact metric spaces that are close together for Gromov-Hausdorff distance, suitable vector bundles on one metric space will have counterpart vector bundles on the other. Our approach employs the Lipschitz constants of projection-valued functions that determine vector bundles. We develop some computational techniques, and we illustrate our ideas with simple specific examples involving vector bundles on the circle, the two-torus, the two-sphere, and finite metric spaces. Our topic is motivated by statements concerning \"monopole bundles\" over matrix algebras in the literature of theoretical high-energy physics.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2008-12-31T18:02:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C23",
      "46L85",
      "55R50"
    ],
    "keywords": [
      "gromov-hausdorff distance",
      "compact metric spaces",
      "counterpart vector bundles",
      "simple specific examples",
      "determine vector bundles"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 66,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8266R"
    }
  }
}