{
  "id": "1408.3859",
  "version": "v2",
  "published": "2014-08-17T21:05:55.000Z",
  "updated": "2014-08-26T18:13:42.000Z",
  "title": "Cocycles of isometries and denseness of domination",
  "authors": [
    "Jairo Bochi"
  ],
  "comment": "26 pages, 3 figures. This version includes a more general result on almost coboundaries and minor presentational changes",
  "categories": [
    "math.DS",
    "math.AT"
  ],
  "abstract": "We consider the problem of approximating a linear cocycle (or, more generally, a vector bundle automorphism) over a fixed base dynamics by another cocycle admitting a dominated splitting. We prove that the possibility of doing so depends only on the homotopy class of the cocycle, provided that the base dynamics is a minimal diffeomorphism and the fiber dimension is least 3. This result is obtained by means of a general theorem on the existence of almost invariant sections for fiberwise isometries of bundles with compact fibers and finite fundamental group. The main novelty of the proofs is the use of a quantitative homotopy result due to Calder, Siegel, and Williams.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-17T21:05:55.000Z",
      "abstract": "We consider the problem of when can a linear cocycle (or, more generally, a vector bundle automorphism) over a fixed base dynamics be approximated by another having a dominated splitting. We show that the answer to this question depends only on the homotopy class of the cocycle, provided that the base dynamics is a minimal diffeomorphism and the fiber dimension is least $3$. This result is obtained as a consequence of a general theorem on the existence of almost invariant sections for fiberwise isometries of bundles with compact fibers and finite fundamental group. The main novelty of the proofs is the use of a quantitative homotopy result due to Calder, Siegel, and Williams.",
      "comment": "26 pages, 3 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-08-26T18:13:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "isometries",
      "domination",
      "vector bundle automorphism",
      "finite fundamental group",
      "main novelty"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.3859B"
    }
  }
}