{
  "id": "1008.1694",
  "version": "v1",
  "published": "2010-08-10T11:33:03.000Z",
  "updated": "2010-08-10T11:33:03.000Z",
  "title": "On the non-existence of certain branched covers",
  "authors": [
    "Pekka Pankka",
    "Juan Souto"
  ],
  "categories": [
    "math.GT",
    "math.AT",
    "math.CV"
  ],
  "abstract": "We prove that while there are maps $\\bT^4\\to\\#^3(\\bS^2\\times\\bS^2)$ of arbitrarily large degree, there is no branched cover from $4$-torus to $\\#^3(\\bS^2\\times \\bS^2)$. More generally, we obtain that, as long as $N$ satisfies a suitable cohomological condition, any $\\pi_1$-surjective branched cover $\\bT^n \\to N$ is a homeomorphism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-10T11:33:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-existence",
      "arbitrarily large degree",
      "homeomorphism",
      "suitable cohomological condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.1694P"
    }
  }
}