{
  "id": "1304.2436",
  "version": "v3",
  "published": "2013-04-09T00:14:59.000Z",
  "updated": "2015-04-13T01:02:23.000Z",
  "title": "$\\mathbb{S}ol^3\\times\\mathbb{E}^1$-manifolds",
  "authors": [
    "J. A. Hillman"
  ],
  "comment": "The earlier version (2013) was fatally flawed. The present version retains only the focus on Seifert fibration as a basis for classification",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "We show that $\\mathbb{S}ol^3\\times\\mathbb{E}^1$-manifolds are Seifert fibred, with general fibre the torus, and base one of the seven flat 2-orbifolds $T, Kb, \\mathbb{A}, \\mathbb{M}b, S(2,2,2,2), P(2,2)$ or $\\mathbb{D}(2,2)$, and outline a classification of such 4-manifolds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-18T00:57:27.000Z",
      "abstract": "We outline a classification of $\\mathbb{S}ol^3\\times\\mathbb{E}^1$-manifolds with $\\beta_1=0$. (The other $\\mathbb{S}ol^3\\times\\mathbb{E}^1$-manifolds are mapping tori, and may be classified in terms of automorphisms of 3-manifold groups.)",
      "comment": "Minor corrections, plus new, short final section showing that all such manifolds bound",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-04-13T01:02:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50"
    ],
    "keywords": [
      "classification",
      "mapping tori"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.2436H"
    }
  }
}