{
  "id": "1302.1137",
  "version": "v1",
  "published": "2013-02-05T18:02:54.000Z",
  "updated": "2013-02-05T18:02:54.000Z",
  "title": "About the homological discrete Conley index of isolated invariant acyclic continua",
  "authors": [
    "Luis Hernández-Corbato",
    "Patrice Le Calvez",
    "Francisco R. Ruiz del Portal"
  ],
  "comment": "35 pages",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "This article includes an almost self-contained exposition on the discrete Conley index and its duality. We work with a local homeomorphism of $\\mathds{R}^d$ and an invariant and isolated acyclic continuum, such as a cellular set or a fixed point. In this setting, we obtain a complete description of the first discrete homological Conley index, which is periodic, that enforces a combinatorial behavior of higher indices. As a consequence, we prove that isolated (as an invariant set) fixed points of orientation-reversing homeomorphisms of $\\mathds{R}^3$ have fixed point index $\\le 1$ and, as a corollary, that there are no minimal orientation-reversing homeomorphisms in $\\mathds{R}^3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-05T18:02:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C25",
      "37B30",
      "54H25"
    ],
    "keywords": [
      "acyclic continuum",
      "isolated invariant acyclic continua",
      "homological discrete conley index",
      "fixed point",
      "first discrete homological conley index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.1137H"
    }
  }
}