{
  "id": "0804.0695",
  "version": "v1",
  "published": "2008-04-04T11:09:48.000Z",
  "updated": "2008-04-04T11:09:48.000Z",
  "title": "A 3-manifold complexity via immersed surfaces",
  "authors": [
    "Gennaro Amendola"
  ],
  "comment": "20 pages, 18 figures, 1 table",
  "journal": "J. Knot Theory Ramifications 19 (2010), no. 12, 1549-1569",
  "doi": "10.1142/S0218216510008558",
  "categories": [
    "math.GT"
  ],
  "abstract": "We define an invariant, which we call surface-complexity, of closed 3-manifolds by means of Dehn surfaces. The surface-complexity of a manifold is a natural number measuring how much the manifold is complicated. We prove that it fulfils interesting properties: it is subadditive under connected sum and finite-to-one on P2-irreducible manifolds. Moreover, for P2-irreducible manifolds, it equals the minimal number of cubes in a cubulation of the manifold, except for the sphere S3, the projective space RP3 and the lens space L41, which have surface-complexity zero. We will also give estimations of the surface-complexity by means of triangulations, Heegaard splittings, surgery presentations and Matveev complexity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-04T11:09:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M20"
    ],
    "keywords": [
      "immersed surfaces",
      "lens space l41",
      "p2-irreducible manifolds",
      "surface-complexity zero",
      "dehn surfaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.0695A"
    }
  }
}