{
  "id": "math/0607099",
  "version": "v3",
  "published": "2006-07-04T18:20:16.000Z",
  "updated": "2007-08-22T20:27:52.000Z",
  "title": "Stability in the Cuntz semigroup of a commutative C*-algebra",
  "authors": [
    "Andrew S. Toms"
  ],
  "comment": "26 pages, minor revisions, to appear in Proc. LMS",
  "doi": "10.1112/plms/pdm023",
  "categories": [
    "math.OA"
  ],
  "abstract": "We prove stability theorems in the Cuntz semigroup of a commutative C*-algebra which are analogues of classical stability theorems for topological vector bundles over compact Hausdorff spaces. Several applications to simple unital AH algebras of slow dimension growth are then given: such algebras have strict comparison of positive elements; their Cuntz semigroups are recovered functorially from the Elliott invariant; the lower-semicontinuous dimension functions are dense in the space of all dimension functions, and the latter is a Choquet simplex.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-08-22T20:27:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L35"
    ],
    "keywords": [
      "cuntz semigroup",
      "dimension functions",
      "simple unital ah algebras",
      "slow dimension growth",
      "commutative"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7099T"
    }
  }
}