{
  "id": "0904.1197",
  "version": "v1",
  "published": "2009-04-07T19:24:18.000Z",
  "updated": "2009-04-07T19:24:18.000Z",
  "title": "On multiplicity of mappings between surfaces",
  "authors": [
    "Semeon Bogatyi",
    "Jan Fricke",
    "Elena Kudryavtseva"
  ],
  "comment": "This is the version published by Geometry & Topology Monographs on 29 April 2008",
  "journal": "Geom. Topol. Monogr. 14 (2008) 49-62",
  "doi": "10.2140/gtm.2008.14.49",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let M and N be two closed (not necessarily orientable) surfaces, and f a continuous map from M to N. By definition, the minimal multiplicity MMR[f] of the map f denotes the minimal integer k having the following property: f can be deformed into a map g such that the number |g^{-1}(c)| of preimages of any point c in N under g is at most k. We calculate MMR[f] for any map $f$ of positive absolute degree A(f). The answer is formulated in terms of A(f), [pi_1(N):f_#(pi_1(M))], and the Euler characteristics of M and N. For a map f with A(f)=0, we prove the inequalities 2 <= MMR[f] <= 4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-07T19:24:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H25",
      "55M20",
      "57M12"
    ],
    "keywords": [
      "minimal multiplicity mmr",
      "minimal integer",
      "euler characteristics",
      "positive absolute degree",
      "continuous map"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.1197B"
    }
  }
}