{
  "id": "1212.4420",
  "version": "v3",
  "published": "2012-12-18T16:43:38.000Z",
  "updated": "2016-11-23T23:07:31.000Z",
  "title": "Homotopical Intersection Theory, III: multi-relative intersection problems",
  "authors": [
    "John R. Klein",
    "Bruce Williams"
  ],
  "comment": "A major revision to the previous version of this preprint. There are now applications to higher dimensional linking as well as to the Goodwillie-Weiss embedding tower",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "This paper extends some results of Hatcher and Quinn beyond the metastable range. We give a bordism theoretic obstruction to deforming a map between manifolds simultaneously off of a collection of pairwise disjoint submanifolds under the assumption that it can be deformed off of any proper subcollection in a homotopy coherent way. In a certain range of dimensions, ours is a complete obstruction to finding the desired deformation. We apply this machinery to embedding problems and to the study of linking phenomena.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-12-20T04:16:24.000Z",
      "abstract": "This paper extends some results of Hatcher and Quinn beyond the metastable range. We give a bordism theoretic obstruction to deforming a map between manifolds simultaneously off of a finite collection of pairwise disjoint submanifolds. In a certain range of dimensions, our obstruction is the entire story.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-11-23T23:07:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N45",
      "57N65",
      "55R70",
      "57R85",
      "57Q45",
      "57R40",
      "57R91"
    ],
    "keywords": [
      "multi-relative intersection problems",
      "homotopical intersection theory",
      "bordism theoretic obstruction",
      "paper extends",
      "finite collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.4420K"
    }
  }
}