{
  "id": "0907.5283",
  "version": "v2",
  "published": "2009-07-30T15:51:43.000Z",
  "updated": "2010-12-17T18:43:48.000Z",
  "title": "Orientation reversal of manifolds",
  "authors": [
    "Daniel Müllner"
  ],
  "comment": "This is the update to the final version. 22 pages",
  "journal": "Algebraic & Geometric Topology 9 (2009) 2361-2390",
  "doi": "10.2140/agt.2009.9.2361",
  "categories": [
    "math.GT"
  ],
  "abstract": "We call a closed, connected, orientable manifold in one of the categories TOP, PL or DIFF chiral if it does not admit an orientation-reversing automorphism and amphicheiral otherwise. Moreover, we call a manifold strongly chiral if it does not admit a self-map of degree -1. We prove that there are strongly chiral, smooth manifolds in every oriented bordism class in every dimension greater than two. We also produce simply-connected, strongly chiral manifolds in every dimension greater than six. For every positive integer k, we exhibit lens spaces with an orientation-reversing self-diffeomorphism of order 2^k but no self-map of degree -1 of smaller order.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-17T18:43:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55M25",
      "57R19",
      "57N65",
      "57S17"
    ],
    "keywords": [
      "orientation reversal",
      "dimension greater",
      "strongly chiral manifolds",
      "diff chiral",
      "smaller order"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.5283M"
    }
  }
}