{
  "id": "math/0505328",
  "version": "v3",
  "published": "2005-05-16T13:22:40.000Z",
  "updated": "2007-03-26T08:59:46.000Z",
  "title": "T-homotopy and refinement of observation (II) : Adding new T-homotopy equivalences",
  "authors": [
    "Philippe Gaucher"
  ],
  "comment": "20 pages, 3 figures",
  "journal": "International Journal of Mathematics and Mathematical Sciences, Article ID 87404, 20 pages, 2007",
  "doi": "10.1155/2007/87404",
  "categories": [
    "math.AT",
    "math.CT"
  ],
  "abstract": "This paper is the second part of a series of papers about a new notion of T-homotopy of flows. It is proved that the old definition of T-homotopy equivalence does not allow the identification of the directed segment with the 3-dimensional cube. This contradicts a paradigm of dihomotopy theory. A new definition of T-homotopy equivalence is proposed, following the intuition of refinement of observation. And it is proved that up to weak S-homotopy, a old T-homotopy equivalence is a new T-homotopy equivalence. The left-properness of the weak S-homotopy model category of flows is also established in this second part. The latter fact is used several times in the next papers of this series.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-03-26T08:59:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U35",
      "55P99",
      "68Q85"
    ],
    "keywords": [
      "refinement",
      "observation",
      "second part",
      "weak s-homotopy model category",
      "old t-homotopy equivalence"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Hindawi",
      "journal": "Adv. High Energ. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5328G"
    }
  }
}