{
  "id": "1901.04734",
  "version": "v1",
  "published": "2019-01-15T09:52:21.000Z",
  "updated": "2019-01-15T09:52:21.000Z",
  "title": "Torsions and intersection forms of 4-manifolds from trisection diagrams",
  "authors": [
    "Vincent Florens",
    "Delphine Moussard"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.GT"
  ],
  "abstract": "Gay and Kirby introduced trisections which describe any closed oriented smooth 4-manifold $X$ as a union of three four-dimensional handlebodies. A trisection is encoded in a diagram, namely three collections of curves in a closed oriented surface $\\Sigma$, guiding the gluing of the handlebodies. Any morphism $\\varphi$ from $\\pi_1(X)$ to a finitely generated free abelian group induces a morphism on $\\pi_1(\\Sigma)$. We express the twisted homology and Reidemeister torsion of $(X;\\varphi)$ in terms of the first homology of $(\\Sigma;\\varphi)$ and the three subspaces generated by the collections of curves. We also express the intersection form of $(X;\\varphi)$ in terms of the intersection form of $(\\Sigma;\\varphi)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-15T09:52:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q10",
      "57M99"
    ],
    "keywords": [
      "intersection form",
      "trisection diagrams",
      "generated free abelian group induces",
      "finitely generated free abelian group",
      "collections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}