{
  "id": "2102.05899",
  "version": "v1",
  "published": "2021-02-11T09:08:20.000Z",
  "updated": "2021-02-11T09:08:20.000Z",
  "title": "A complexity of compact 3-manifold via immersed surfaces",
  "authors": [
    "Gennaro Amendola"
  ],
  "comment": "19 pages, 11 figures, 1 table. arXiv admin note: substantial text overlap with arXiv:0804.0695",
  "categories": [
    "math.GT"
  ],
  "abstract": "We define an invariant, which we call surface-complexity, of compact 3-manifolds by means of Dehn surfaces. The surface-complexity 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 $\\mathbb{P}^2$-irreducible and boundary-irreducible manifolds without essential annuli and M\\\"obius strips. Moreover, for these manifolds, it equals the minimal number of cubes in a cubulation of the manifold, except for the sphere, the ball, the projective space and the lens space $\\mathbb{L}_{4,1}$, which have surface-complexity zero. We will also give estimations of the surface-complexity by means of ideal triangulations and Matveev complexity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-11T09:08:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M20"
    ],
    "keywords": [
      "immersed surfaces",
      "matveev complexity",
      "lens space",
      "dehn surfaces",
      "natural number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}