{
  "id": "math/9901085",
  "version": "v2",
  "published": "1999-01-21T02:20:56.000Z",
  "updated": "2001-07-10T11:52:04.000Z",
  "title": "Immersed and virtually embedded pi_1-injective surfaces in graph manifolds",
  "authors": [
    "Walter D. Neumann"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-20.abs.html",
  "journal": "Algebr. Geom. Topol. 1 (2001) 411-426",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that many 3-manifold groups have no nonabelian surface subgroups. For example, any link of an isolated complex surface singularity has this property. In fact, we determine the exact class of closed graph-manifolds which have no immersed pi_1-injective surface of negative Euler characteristic. We also determine the class of closed graph manifolds which have no finite cover containing an embedded such surface. This is a larger class. Thus, manifolds M^3 exist which have immersed pi_1-injective surfaces of negative Euler characteristic, but no such surface is virtually embedded (finitely covered by an embedded surface in some finite cover of M^3).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-07-10T11:52:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M10",
      "57N10",
      "57R40",
      "57R42"
    ],
    "keywords": [
      "negative euler characteristic",
      "finite cover",
      "isolated complex surface singularity",
      "nonabelian surface subgroups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......1085N"
    }
  }
}