{
  "id": "1707.02450",
  "version": "v1",
  "published": "2017-07-08T14:50:59.000Z",
  "updated": "2017-07-08T14:50:59.000Z",
  "title": "Cobordism groups of simple branched coverings",
  "authors": [
    "Csaba Nagy"
  ],
  "comment": "30 pages, 3 figures. Submitted to Acta Mathematica Hungarica",
  "categories": [
    "math.GT"
  ],
  "abstract": "We consider branched coverings which are simple in the sense that any point of the target has at most one singular preimage. The cobordism classes of $k$-fold simple branched coverings between $n$-manifolds form an abelian group $Cob^1(n,k)$. Moreover, $Cob^1(*,k) = \\bigoplus_{n=0}^{\\infty} Cob^1(n,k)$ is a module over $\\Omega^{SO}_*$. We construct a universal $k$-fold simple branched covering, and use it to compute this module rationally. As a corollary, we determine the rank of the groups $Cob^1(n,k)$. In the case $n = 2$ we compute the group $Cob^1(2,k)$, give a complete set of invariants and construct generators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-08T14:50:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R45",
      "57R90",
      "57M12"
    ],
    "keywords": [
      "cobordism groups",
      "fold simple branched covering",
      "singular preimage",
      "construct generators",
      "manifolds form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}