{
  "id": "2002.08485",
  "version": "v1",
  "published": "2020-02-19T22:41:04.000Z",
  "updated": "2020-02-19T22:41:04.000Z",
  "title": "The Minimal Genus of Homology Classes in a Finite 2-Complex",
  "authors": [
    "Thorben Kastenholz",
    "Mark Pedron"
  ],
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "We study surface representatives of homology classes of finite complexes which minimize certain complexity measures, including its genus and Euler characteristic. Our main result is that up to surgery at nullhomotopic curves minimizers are homotopic to cellwise coverings to the 2-skeleton. From this we conclude that the minimizing problem is in general algorithmically undecidable, but can be solved for 2-dimensional CAT(-1)-complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-19T22:41:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R95"
    ],
    "keywords": [
      "homology classes",
      "minimal genus",
      "study surface representatives",
      "nullhomotopic curves minimizers",
      "euler characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}