{
  "id": "1909.13187",
  "version": "v1",
  "published": "2019-09-29T02:06:50.000Z",
  "updated": "2019-09-29T02:06:50.000Z",
  "title": "Equivalence Relations Between Closed Curves On the Pair of Pants",
  "authors": [
    "Nithin Kavi"
  ],
  "comment": "17 pages, 10 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We examine an equivalence relation between free homotopy classes of closed curves on the pair of pants known as k-equivalence, a generalization of a concept previously defined by Leininger. We prove that two classes of closed curves on the pair of pants that are k-equivalent must also be 1-equivalent and 2-equivalent. We also examine properties of 1-equivalence on the pair of pants in greater depth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-29T02:06:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50"
    ],
    "keywords": [
      "closed curves",
      "equivalence relation",
      "free homotopy classes",
      "greater depth",
      "k-equivalence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}