{
  "id": "1709.09040",
  "version": "v1",
  "published": "2017-09-24T22:48:04.000Z",
  "updated": "2017-09-24T22:48:04.000Z",
  "title": "Gauss--Bonnet theorem for compact and orientable surfaces: a proof without using triangulations",
  "authors": [
    "Romero Solha"
  ],
  "comment": "9 pages",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "The aim of this note is to provide a proof of the Gauss--Bonnet theorem without invoking triangulations, which is achieved by exploiting (almost) complex structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-24T22:48:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A99",
      "30F99"
    ],
    "keywords": [
      "gauss-bonnet theorem",
      "orientable surfaces",
      "complex structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}