{
  "id": "1502.04338",
  "version": "v1",
  "published": "2015-02-15T17:44:21.000Z",
  "updated": "2015-02-15T17:44:21.000Z",
  "title": "Some Results on Pseudo-Collar Structures on High-Dimensional Manifolds",
  "authors": [
    "Jeffrey Rolland"
  ],
  "comment": "69 pages, no figures. This is my PhD thesis. A more concise version is being prepared for publication",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we recall Quillen's plus construction for high-dimensional smooth manifolds and the solution to the group extension problem. We then develop a geometric procedure due for producing a \"reverse\" to the plus construction, a one-sided s-cobordism called a semi-s-cobordism, when the total group of the group extension is a semi-direct product. We then use this reverse to the plus construction to produce uncountably many different one-ended manifolds called pseudo-collars, which are stackings of semi-s- cobordisms. We finally display a technique for producing \"nice\" one-ended open manifolds which satisfy two of the necessary and suffcient conditions for being pseudo-collarable but not the third.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-15T17:44:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R90"
    ],
    "keywords": [
      "high-dimensional manifolds",
      "pseudo-collar structures",
      "recall quillens plus construction",
      "high-dimensional smooth manifolds",
      "group extension problem"
    ],
    "tags": [
      "dissertation"
    ],
    "publication": {
      "journal": "Ph.D. Thesis",
      "year": 2015
    },
    "note": {
      "typesetting": "TeX",
      "pages": 69,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015PhDT........59R"
    }
  }
}