{
  "id": "2108.08379",
  "version": "v1",
  "published": "2021-08-18T20:35:46.000Z",
  "updated": "2021-08-18T20:35:46.000Z",
  "title": "Combinatorial $k$-systoles on a punctured tori and a pairs of pants",
  "authors": [
    "ElHadji Abdou Aziz Diop",
    "Masseye Gaye",
    "Abdoul Karim Sane"
  ],
  "comment": "12 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, $S$ denotes a hyperbolic surface homeomorphic to a punctured torus or a pairs of pants. Our interest is the study of \\emph{\\textbf{combinatorial $k$-systoles}} that is geodesics with self-intersection number greater than $k$ and with minimal combinatorial length. We show that the maximal intersection number $I_k$ of combinatorial $k$-systoles grows like $k$ and $\\underset{k\\rightarrow+\\infty}{\\limsup}(I_k(S)-k)=+\\infty$. This answer -- in the case of a pairs of pants and a punctured torus -- a weak version of Erlandsson-Palier conjecture, originally stated for the geometric length.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-18T20:35:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "punctured torus",
      "hyperbolic surface homeomorphic",
      "maximal intersection number",
      "minimal combinatorial length",
      "self-intersection number greater"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}